United Nations, N.Y. — Russian playwright Anton Chekhov's ''Seagull'' was recently staged in Peking. In Heilongjiang province along the Sino-Soviet border, Russian is once again taught in the schools alongside English. Chinese journalists may be soon based in Moscow and vice versa. And a Soviet chess team is now expected in Peking.
These improvements in Sino-Soviet atmospherics foreshadow a slow but substantial political thaw, in the opinion of China watchers here.
The show of mutual interest between China and the Soviet Union is not merely temporary or tactical, according to these well-placed diplomats at the United Nations.
Furthermore, both Peking and Moscow now see their relationship as independent of the United States and judge each other on their own merits.
Even so, as China and the Soviet Union have started talks aimed at ending two decades of hostility, no great breakthrough is expected. Fundamental problems - rooted in deep and lasting national interests - will remain. Sino-Soviet relations will never again be what they were in the 1950s.
And there are no signs that the three major obstacles to full normalization of Soviet-Chinese relations can be removed in the near future. China insists that Vietnam leave Kampuchea, that Soviet troops be pulled out of Afghanistan, and that Soviet troops be withdrawn from the Chinese border until border claims between the two nations are settled.
Despite all this, according to one diplomat, ''Just as China had put the Taiwan question between brackets and normalized its relations with the US, it could normalize its relations with the USSR and put the three contentious subjects between brackets.''
Last fall China first made direct overtures to the Kremlin when it agreed to hold regular consultations with Soviet officials aimed at normalizing relations. On Dec. 26, the Chinese leadership sent a message to Moscow stressing the necessity for both governments to show flexibility. Soon after that, for the first time in more than two decades, Soviet leaders started referring to China as ''a socialist country.''
At Leonid Brezhnev's funeral, Soviet premier Yuri Andropov caused a diplomatic stir when he stopped to talk with China's then-Foreign Minister Huang Hua. The talks which began last week in Moscow between Leonid Ilyichov and Qian Qichen, the Soviet and Chinese deputy ministers of foreign affairs, were put on track when Mr. Ilyichov spent three weeks in Peking last October.
And even before these high-level talks, a leading Soviet specialist in Chinese affairs, Boris Riftin, spent six months in China visiting Chinese universities, with the agreement of China's government. When he returned to Moscow, he gave 42 lectures to Soviet scholars, officials, and top Communist Party members about ''Chinese perceptions of the Soviet Union.''
Reportedly, the gist of these lectures was that Chinese perceptions are far from being as negative as had been believed in the Soviet Union. Meanwhile, two Chinese scholars were visiting the USSR as guests of Gosplan or the State Planning Commission and, according to informed sources, gave their government ''a positive assessment of Soviet efforts in the economic field'' and an encouraging view of possible Soviet-Chinese trade increases. Sino-Soviet trade, totaling $320 million in 1982, increased by 46 percent over 1981 and is expected to increase dramatically in 1983 by experts.
China's desire to normalize relations with the Soviet Union can be attributed to the following reasons:
* China's top priority is modernization of its economy. Toward this end, it needs, 1) a peaceful environment including, less tensions with its powerful northern neighbor; 2) all the economic and trade benefits it can get, and, to this effect, a larger presence in the world and a more dynamic, diversified diplomacy. Economic relations with the US remain important but must be complemented by trade relations with the USSR and many third-world countries.
* China is relatively disppointed with its US relations. ''Peking has paid a heavy political price for relatively small economic benefits,'' says one China hand. China has not been able to import high-technology goods it wants from the US. The US has not helped modernize the Chinese armed forces. It imposes a 1.6 percent increase on Chinese textile imports, whereas China considers that a 6 percent rise would be in line with US practice toward other friendly countries. The Reagan administration's pro-Taiwan tilt has irritated the Chinese leadership. Meanwhile, by being perceived in the third world as a de facto ally of the US, China's image has been tarnished somewhat.
* China is adopting a more nonaligned stance in foreign policy. It noticeably changed gears in October 1981 when voting against Kurt Waldheim for a third term as secretary-general of the United Nations, throwing its support to Tanzania's Salim Salim. China's prime minister Zhao Ziyang's recent tour of Africa, where he visited 10 capitals, was aimed at stressing China's renewed interest in the third world. However, China's new ''third-worldism'' is less radical, less ideological than was its first version 25 years ago.
* China is playing down ideology in its relations with the US and the USSR. Its leaders are assessing both superpowers more realistically than before. Essentially, what China wants is more room for maneuver, Chinese officials admit. ''Triangular politics is a game three can play,'' says an Asian diplomat who follows China's foreign policy closely. ''The Chinese have now taken a page from (Henry) Kissinger's book: By appearing to be on good terms with both Moscow and Washington, they keep both superpowers guessing and thus strengthen their own hand,'' he says. The Chinese like to call their new foreign policy ''independent.'' But this new diplomacy is not isolationist as in the early 1960 s; it is more internationalist and aimed at diversification.
* Ideologically, China and the USSR are no longer quarreling. In the past, Moscow equated ''Maoism'' with ''Nazism.'' To China's Maoists, the Soviets were ''social Fascists.'' China's present government is ''centrist'' in such ideological disputes, and similar in many ways to the Soviet regime. And while party-to-party relations are expected to remain cool, state-to-state relations may improve, especially since ideology is not now a priority issue for either side.
* The USSR wants to reduce tension with China. The Kremlin confronts the fighting spirit of the Reagan administration, major difficulties in Afghanistan and Poland, and a sluggish Soviet economy. It also may want to reduce the military burden in the Far East and gain some breathing space strategically, diplomatically, and economically.