At the time that Spain was admitted to NATO, no new members had been admitted since West Germany in 1955. So why did it take about three decades longer for Spain to be admitted than West Germany or the original members such as France, Italy, or even their neighbor Portugal?

Francisco Franco's regime controlled Spain from 1939 until his death in 1975, but the exclusion of Spain from NATO had to do much more with the views of the other member states rather than Franco's policies. The overthrow of the 2nd Spanish Republic in the civil war and subsequent violent repression of his political enemies (both real and perceived), to say the least, soured relations with western democracies for decades to come. And, of course, despite Spain's official neutrality in WWII, Franco shared much more in common ideologically with Germany than with the Allies.

After the war, however, Franco proved willing to band with the victors against Bolshevism, their common foe. Spain was denied membership at the foundation of the UN in 1945 for as long as Franco remained in power, however, and also was excluded from the Marshall Plan despite their economic difficulties. But as the Cold War developed, the United States decided to normalize relations with Spain, even if it meant working with Generalissimo Franco. The Pact of Madrid, signed in 1953, provided military and economic aid to Spain from the US. Spain was finally admitted into the UN two years later.

Despite Franco's efforts to join both NATO and the European Economic Community (EEC, which would eventually be subsumed into the EU), Francoist Spain was never admitted to either. Franco formally applied to join the EEC in 1962 but was declined, and an attempt by the United Stated to get Spain into NATO as late as 1975 was also rejected by the other member states.

Franco's death in 1975, and his successor King Juan Carlos I's turn towards democracy finally paved the way for Spain's entry into NATO. The general election of 1977 installed an elected Cortes as the legitimate government, with a majority under Adolfo Suarez and the UCD (Union of the Democratic Center). The Cortes' newfound authority was shaky at first, and suffered its greatest test during the attempted military coup on 23 February, 1981, but after an address by Juan Carlos I the military stood down, having lost hope for popular support. The election of 1981 saw the UCD retain control under Leopoldo Calvo-Sotelo, who made admission into NATO (and by association, later admission into the EEC) a priority. Spain's growing minority party, the PSOE (Spanish Socialist Workers' Party) was opposed to joining NATO, citing concerns about becoming an easy target if the Cold War turned hot. But despite internal dissent in Spain, as well as concerns about violence surrounding Basque separatism (ETA), the member states of NATO were finally willing to admit Spain in 1982.

P.S. A snap election in 1982 gave the PSOE a majority after they had run in part on a platform of staying out of NATO, but Spain ultimately decided to remain in NATO after a 1986 referendum revealed a majority of voters desired to remain in the treaty organization. This vote had occurred only a few months after Spain's admission into the EEC, and it is possible that the voters believed that if they left NATO they might also be kicked out of the EEC.

Not an answer, but a counter question. As opposed to what? Are you asking why Francoist Spain was not in NATO? Or why it did not happen immediately after Spain became a democracy?