PARIS -- Mikhail Gorbachev, Washington's Guest of the Year in 1987, is back at the grindstone in Moscow urging the Soviet media to shape up and push perestroika. His need to do this a month after his roadshow success in America brings us (and him) back to the central reality of Soviet leadership, which was obscured by the glitter and glare of the Washington summit.

Lecturing, negotiating, even singing along, Gorbachev Super Czar dazzled the media and impressed the powerful in Washington. President Reagan and Secretary of State George Shultz spoke of Reagan and Gorbachev working together to change the world. "Maybe we could help him . . . get his glasnost," Reagan told television interviewers.

But when Gorbachev called senior editors and cultural figures together last week in the Kremlin, the divided nature of Gorbachev's power at home was again on display. Hovering at his elbow during this vital ideological pep talk was Yegor Ligachev, who has emerged in recent months as both Gorbachev's main partner in the Politburo -- and the only clear alternative to him.

"Americans tend to see other political systems as extensions of their own very personalized politics," centering on one man who either commands or is losing power to a rival, says Michel Tatu, one of France's leading Kremlinologists. "But the Soviet system is much more collective than personal."

Tatu's new book, "Gorbachev," has just been published and has quickly become a must read for foreign affairs buffs here.

Tatu says that events since he put the finishing touches on the book in November have reinforced his judgment that Ligachev "has become more of a Number One and One-Half rather than a Number Two." He does not want to go in a different direction than Gorbachev, but he would like to get there much slower and without upset.

Ligachev visited Paris on the eve of the Washington summit and disclosed in a revealing interview with Tatu that he, and not Gorbachev, chairs the meetings of the Central Committee's all-powerful Secretariat. Ligachev repeated this when asked the same question at a press conference here on Dec. 4.

But, interestingly enough, that question and answer were omitted when the press conference was reproduced in the Soviet media. And a few days later in Washington, an aide to Gorbachev told a U.S. official that Ligachev's statement was inaccurate. (It has been publicly confirmed since then by other Soviet officials asked about it by western journalists.)

This is a sign of sensitivity to the power-sharing arrangement at the core of Kremlin politics, and not of a current power struggle. As Tatu's book notes, at a time of great change in the Soviet system "anyone who is Number Two becomes the alternative, even without wanting it, for all those who are not pleased" by the changes undertaken in the name of the leader.

But he also notes that "until the Number One can choose his own Number Two, he cannot have unchallenged authority." Gorbachev will achieve that only when he can put Alexander Yakovlev, his closest ally on the Politburo, into the second spot.

Watching Ligachev conduct a press conference in Paris and then witnessing Gorbachev perform the same task in Washington a few days later in December left me with a sense of two very powerful, self-assured men who are in complete agreement on foreign policy, have reached general agreement on the need for urgent administrative reform and a shakeup of the stultified Soviet economic bureaucracy, and are only in limited agreement over the wisdom of "glasnost" and "democratization" at home.

In Washington, Gorbachev kept Yakovlev at his side during the press conference and asked him "to conduct this auction." In Moscow, Yakovlev was absent from Gorbachev's meeting with the Soviet media while Ligachev was highly visible. East European sources are persuaded that Ligachev has taken on the dominant role in internal propaganda, while Gorbachev's chief ally is to concentrate on foreign propaganda strategies.

The policy implications of such a division of authority are highly important. The Washington summit made it clear that Gorbachev can bring his colleagues along on arms control and foreign policy in general. The Moscow media meeting suggests that when it comes to the human rights problems that Shultz says must also improve if Soviet-U.S. relations are to have a strong foundation, it is the more conservative Ligachev who increasingly calls the shots on the Politburo. There should be no illusions in Washington about the unpromising meaning of that.