Peking — Gone are the days when it looked as though the United States and China were headed for an era of strategic cooperation against the Soviet Union amounting virtually to an alliance.
This was the dream of three key foreign policy makers who helped to shape China policy in the past: Henry Kissinger, Zbigniew Brzezinski, and Alexander M. Haig Jr.
Today the aims are more tempered. In his quiet way, US Secretary of State George Shultz is attempting to restore momentum to a US-China relationship that has deteriorated since the Reagan administration came to office.
Both sides have attempted to set a conciliatory tone as the talks
begin here. Each party seems to be groping to find a new and more realistic basis for their relationship. Mr. Shultz in particular is convinced that the two nations have ''parallel interests'' in a number of areas.
There were times in the past when a trip to Peking by an American secretary of state seemed almost like a pilgrimage. A trip to the Great Wall of China was part of the ritual. The visitor looked out toward the wastes from which came the threatening hordes. The US and China faced a common enemy. In a joking mood, Mr. Brzezinski even raced to the wall, allowing that he who was the last to arrive would have to fight the Russians.
Since that outburst of enthusiasm, both sides have calmed considerably. The Soviets have got themselves tied down in Afghanistan and Poland and apparently seem slightly less threatening to the Chinese. The American connection has not paid off as handsomely as the Chinese had hoped it would, either in high technology or in other forms of economic cooperation. And Ronald Reagan, an admirer of Taiwan, is a difficult man to deal with in Chinese eyes.
But both sides are now acting as though the deterioration in relations has gone far enough. Secretary Shultz is attempting to restore momentum by focusing on common interests. He wants to clear up misunderstandings. He is ready to talk about cooperation in many fields. He professes to be exhilarated by being in China for the first time. But he is going about all this in a sober, matter-of-fact way which implies a break with what some call ''the Great Wall syndrome'' - the romanticism of the past.
Indeed, Shultz is so busy here with four days of meetings Feb. 2-6 that he may have no time at all to visit the Great Wall, that symbol of China's strength and unity.
When Shultz's predecessor, General Haig, came here in 1981, he made it sound like the US would soon begin selling to China on a case-by-case basis certain ''defensive'' military equipment. That idea fell through after President Reagan reaffirmed his support for Taiwan. Within hours after Haig made declarations on the subject of military sales in Peking, Reagan effectively cut Haig off at the knees.
Shultz is more cautions when it comes to the subject of military equipment for China. En route to Peking from Tokyo aboard an Air Force plane on Tuesday Feb. 2, Shultz answered a question regarding such sales: ''I'm prepared to discuss what needs they may have but in the framework of earlier discussions, which essentially emphasized defensive problems and on which nothing much has happened. So maybe there isn't anything on anybody's mind, but if there is. . . .''
In a banquet toast that same evening, Shultz declared that the US and China share ''many parallel interests'' and ''have great potential for influencing positively the course of world events.'' He said that President Reagan had asked him to repeat ''his strong personal commitment to the advancement of US-China relations.'' And Shultz spoke of the importance of ''a strong and lasting US-China relationship in confronting the economic and strategic challenges that threaten the well- being of all.''
In his toast, Shultz's Chinese counterpart, Wu Xueqian, declared that China ''will firmly adhere to the policy of opening to the outside world economically and actively increase exchanges and cooperation with other countries on the basis of equality and mutual benefit.'' He advocated stability in the world as a basis for China's economic modernization program.