This is actually why we use the term "liberal democracy" when describing what we would just call "democracy" in our daily language, as proponents of both fascism and communism perceived these forms of government as being more democratic than "liberal," "Western," or "bourgeoisie" democracy (all three terms mean essentially the same thing). Fascists and Communists both believed that their forms of government represented the will of the people, in juxtaposition to bourgeoisie democracy, which represented the will of the very rich people. This is a criticism that we see throughout the twentieth century even within liberal democracies themselves. And keep in mind that the Soviet model was, in a sense, democratic--sure, you could only vote for members of the Communist Party, and those in power could block potential candidates from running for office, but these were restraints that true believers (and there were plenty of them) thought were necessary to prevent "counterrevolution" and the return to bourgeoisie democracy. Local factories and other organizations that represented the working class could and did nominate potential candidates for local office, and successful politicians who made it onto the state's Central Committee tended to have the support of a local population in addition to the party apparatus. On top of that, the central organization that ruled over Eastern Bloc nations, the "politburo" or "presidium," in some key ways was democratic. The members were selected by the Central Committee, and while in practice the politburo often selected its members and the Central Committee's vote was a sort of rubber stamp, rebellion from a Central Committee really could change the face of a politburo, as was the case in Czechoslovakia in 1968 (the "Prague Spring").

If you remain unconvinced that this system really was "democratic," that's fine--I even agree with you. But the fact remains that the GDR had an ideological claim to being a "truly" democratic nation, even if it did not live up to that ideal.

Modified from an earlier answer of mine

The following answer really only applies to the Soviet bloc. I suspect the DPRK followed something similar, but the DPRK styled itself as a maverick even within the confines of both Maoism and Marxist-Leninism, so it is possible that the electoral process was quite different.

The orthodox Marxist-Leninist position on elections and democracy was quite complicated. On one hand, the official position of many communist parties in the twentieth century was that they were the will of the people and they had nothing to fear from elections. Conversely, communist ideologues often stressed that liberal democracy was incompatible with the true interests of the toiling masses over the long-term. As the entry on democracy in the 1979 Great Soviet Encyclopedia claimed:

Bourgeois democracy—the most highly developed historical type of democracy in an exploiter society—is a form of dictatorship of the capitalists over the proletariat and other semiproletarian and nonproletarian toiling classes and strata of the population. It is characterized by a manifest contradiction between the declared "rule by the people" and the actual dominion of the exploiters. The functions of the institutions of bourgeois democracy consist in ensuring a class dominance that guarantees the privileges of the exploiter class and disguising its dominion, consolidating the class of the bourgeoisie, and solving its own internal class contradictions. This interpretation of bourgeois democracy by Marxism-Leninism does not signify an absolutely negative assessment of it: a democracy, even if it is only a formally declared one, is of significant value, since in conditions of democracy the framework of political freedom and independent social and individual activity is incomparably broader than in conditions of authoritarianism and other nondemocratic regimes.

In this teleology, liberal democracy is a way station towards a people's democracy, but it also has the potential to devolve into fascism.

This bifurcated view of the democratic process led to a somewhat peculiar form of elections and party process both in the Soviet Union and the Eastern bloc. Although they were all de facto one-party states and a highly authoritarian ones at that, their constitutions often made provisions for elections and voting. In the USSR, the Stalin Constitution of 1936 had sections guaranteeing free elections and the Stalinist state staked a good deal of its legitimacy upon high turn-out during elections. The Stalin Constitution remained in force until 1977, when Brezhnev ordered a new constitution which was a document much like its predecessor. Article 3 of the GDR's constitution affirmed that all citizens of the state had the right to participate in the political life of the nation and the ability to vote and stand for elections.

Such elections were usually towards legislative bodies from a list of candidates. The USSR set the pace for much of the Eastern bloc's legislative process. Most Soviet citizens had to vote for delegates to the Supreme Soviet, the major parliamentary body in the USSR. Although both the 1936 and 1977 constitutions imbued the Supreme Soviet with broad, sweeping powers, in practice, the Supreme Soviet was a toothless rubber stamp for the choices of the executive central committee of the Party. The constitutions allowed candidates from outside the Communist Party to stand for elections to the Supreme Soviet, but they usually had to be nominated or approved by their local Communist Party apparatus. There were detailed guidelines from Moscow about acceptable candidates and the state forbid adversarial electioneering campaigns. More often than not, voters usually had a choice of a single candidate, especially after the 1977 constitution. Elections were called by the Presidium of the Supreme Soviet at regular scheduled intervals and took place in districts designated by the state.

This process was replicated in the Eastern bloc with several variations. The GDR, by virtue of its competition with the FRG, had something close to a multi-party system with four minor parties in addition to the ruling SED. Czechoslovakia had the Československá strana lidová (CSL) and Poland the Stowarzyszenie PAX which were nominally Christian Social and Catholic parties respectively. These minority parties were to represent those social groups and individuals who did not quite fit into the class picture of the main Communist party. They also served as a counterpoint to the West showing the true nature of a people's democracy. Many of these minority parties had direct analogues in the West, such as the FRG's CDU, which even shared an identical name with its GDR counterpart. Domestically, the minority parties served a more sinister purpose of neutering social groups like the churches by keeping a tight lid on their political expression within the state and having the majority parties' own creatures in positions of limited power.

These systems led to an aspersion in the West that Eastern bloc elections were "elections without choice," and there is a great deal of truth in this charge. However, this charge can obscure the inordinate degree of attention Eastern bloc regimes lavished upon elections. The Stalin Constitution nominally provided for a secret ballot and a degree of candidates and other Eastern bloc states used high electoral turnout to legitimize the grand communist experiment. The 1977 constitution also decreed an election's results to be invalid if turn out was low. High turnout was also a means of social control by the state as elections verified that the voter was a legal resident of a particular area. In the GDR, whose security authorities were justifiably leery of the loyalty of the population, there was extensive surveillance of who voted and which Germans had abstained. Therefore, local officials were often under intense pressure to guarantee a high political turnout for both propaganda and practical purposes. This was one of the reasons why voter turnout in the USSR typically averaged in the eightieth percentile from 1937 onward and such numbers were quite typical for the rest of the bloc.

While many local CP officials fudged the numbers of turnout, this was a dangerous stratagem for an apparatchik if caught. Unlike fascist or right-wing authoritarian plebiscites, researchers into Eastern bloc elections have found the turnout numbers to be more or less accurate. Much like political bosses in the West, these local officials preferred to employ various inducements to get voters to the polls over chicanery. From the Second World War onward, Eastern bloc elections increasingly assumed a holiday-like atmosphere to attract voters. Similarly, mobile voting booths were often used to make sure that infirm voters or those in distant regions could cast their ballots. The festivals were an opportunity by the state to build up faith in its brand of socialism and create a type of political collectivity that its security forces often told them did not exist.

The intense pressure from the center on these local officials to deliver the numbers gave the Eastern bloc voter leverage in which abstaining from voting gave the voter a degree of power than actually voting. Voting against a candidate, such as scratching out the name, was an embarrassment to the local CP officials and detrimental to their careers. The various meetings in the run-up for Eastern bloc elections were often a time when the public could petition the officials for local improvements, repair of infrastructure, and airing other grievances. There was also a pronounced uptick in petitions and other requests to the electoral officials and newspapers during election season and some of these entreaties included the threat that if they were not met by election day, these individuals would boycott the election. By the same token, some voters would sometimes write petitions on the ballots to the authorities with the assumption that the higher ups would read them. Some of these preserved ballots have patriotic slogans, but others contained personal requests or denunciations of local officials.

Although Eastern bloc elections were not democratic in any common meaning of the word, they were an anemic channel for political communication between the state and its citizens. Over the long-term, these "elections without choice," did foster an apathy over the Communist system and its many hypocrisies, but they did also provide a mechanism to cope with the grim reality of a single-party state. Even without any real electoral choice, many Soviet citizens recognized that there was some degree of power in the act of voting and bargained with local officials accordingly.

Sources

Jessen, Ralph, and Hedwig Richter. Voting for Hitler and Stalin: Elections Under 20th Century Dictatorships. Frankfurt: Campus Verlag, 2011.

Sakwa, Richard. Soviet Politics in Perspective. London: Routledge, 1998