I've wondered this ever since I found a Melodiya copy of Bon Jovi's "New Jersey" in a used record store. (Specifically Fred's in St. John's, Newfoundland, where Soviet fishing vessels were once common.) Did the USSR pay royalties to the Western record companies and artists, or were they basically state-sponsored bootlegs?
The record released by Melodiya were not state-bootlegs, but was an officially licensed product. Established in 1964, Melodiya was the state-enterprise for the production and release of musical recordings in the USSR and it had a near monopoly on recording. As such, it had a degree of weight behind it and it was able to negotiate with Western music labels for the rights to print and distribute music performed by Western artists.
The history leading up to the Soviet Bon Jovi's New Jersey is rather interesting. Like many cultural enterprises in the Cold War Soviet Union, Melodiya was to be a source of general cultural uplift and a means to present music to the masses. Often times this meant Melodiya often produced either classical or folk music, as well as ideological material like Brezhnev speeches. A number of Soviet cultural authorities in the late 1960s and 70s were often quite leery of Western rock music, not only because it was decidedly "uncultured," but because there was a fear that the Western artists' appeals for free love and the various drug references was an attempt by the capitalist West to subvert global youth culture with an appeal to hedonism. But increased contacts with the West led to a proliferation of bootlegs, most famously the so-called bone music impressed on x-ray film, so the state elected to try and control the flow of Western music through entities like Melodiya. At first, Melodiya printed nominally safe music like disco and jazz. Melodiya's large catalog of classical music initially gave it a degree of leverage with labels like CBS which had a large classical division. Melodiya managed to reach a reciprocal deal with Columbia, Epic, and CBS in 1974 in which the Western companies received classical music like Prokofiev and Melodiya would release records by Miles Davis, Ray Conniff, and Ella Fitzgerald.
These type of trade deals led to the gradual penetration of Western pop music into the USSR through official state channels. As trade patterns normalized between the West and the USSR, Western companies began to increasingly ask for hard currency for Western music, which led Melodiya to be somewhat selective in its licensing. According to a 1979 Billboard report, Melodiya's 1978 catalog had some 30000 titles, with 34% of it classical, 20 % pop, easy listening and jazz, 12% Soviet folk music, and the remainder children's music and spoken word or historical materials. By the 1980s, Melodiya increasingly began to use its pop imprints, both Soviet and Western, to pay for its more esteemed classical productions. The result was Melodiya was a Soviet institution well-primed for both Glasnost and Perestroika in that it had an incentive to keep open the channel to the West. In 1986, Melodiya managed to sign a deal with EMI for an official imprint for the Beatles in an effort to curb bootlegging. But the openness of the Gorbachev era worked both ways and Melodiya found itself under increasing attack for the poor quality of its products and the narrowness of its catalog in actual material Soviet consumers wanted. The result was that Melodiya began to deal directly with Western acts in conjunction with their normal deals with Western recording companies. This was where New Jersey entered the picture as it was a byproduct of Melodiya's desire to produce Western music, but also control its flow and content. The Soviets brought in Bon Jovi for a concert in Moscow in conjunction with its release of New Jersey. Bon Jovi was an ideal candidate for this step as Richie Sambora said in a 1989 Rolling Stone piece about the concert "We're safe. We're not heavy metal, but we're certainly not pussy rock, either."
As Sambora's rather stereotypical swagger shows, Melodiya was caught between the horns of a dilemma. Although it was always leery of producing sales figures, Melodiya's heads knew that it was its pop imprints that had the highest demand even though it was intended as a means of state-sponsored enlightenment. The more it tried to regulate and control this demand, the more the state-sponsored entity encouraged the consumption of Western music and its own cultural activities looked feeble and sclerotic in comparison.
Sort of on the same subject I'd highly reccomend Jeremy Deller's The Posters Came From The Walls. It's a documentary about obsessive Depeche Mode fans. A lot of the coverage is about how fans in the Eastern Block countries were able to obtain and distribute Depeche Mode records back in the 80s, as well as modern day Iranian fans doing the same. Fascinating stuff.