Peking — Shaking hands in the Great Hall of the People, Deng Xiaoping, communist reformer, and Ronald Reagan, capitalist roader, have built a bridge for a more stable and vigorous relationship between the United States and the People's Republic of China.
Relations got off to a rocky start when President Reagan first came into office. Now they are back on track with mutual pledges to expand economic and technological cooperation, even though such sensitive issues as Taiwan still divide the two countries.
''The commitment to stand as friends has been made,'' the President declared in a banquet toast. ''The promise is solid. The challenges that remain, however, will take both patience and mutual understanding.''
In the thinking of Chinese leaders, the mere fact of the presidential visit is paramount. Asked if any progress had been made in the 11/2 hour meeting with Mr. Reagan, senior Chinese leader Deng replied: ''Much progress has been made. The most important progress is that I met the President the first time.''
From the President's standpoint, the visit is expected to have political as well as diplomatic benefits. Mr. Reagan demonstrated that he is able and willing to deal realistically with communist leaders, thereby reassuring those Americans who are concerned that his strong anticommunism could lead to conflict. Yet by solidifying Sino-American relations, Reagan may have laid the basis for enhanced stability in a region where the Soviets are expanding their presence.
Now that the official portion of his visit is over, the President is spending the remainder of his time in China sightseeing. On Sunday the Reagans flew to Xian, the ancient capital of China, where they viewed the magnificant terra-cotta figures unearthed at the Qin Shihuang tomb. Later asked his impressions, Reagan responded, ''I think it's hard to absorb all at once. I'd better think about it a long time.''
The visit throughout has been diplomatically impeccable. The Chinese have been gracious and cordial. But after some eight hours of meetings between Reagan and top Chinese leaders, including Premier Zhao Ziyang and Communist Party General Secretary Hu Yaobang, it is clear that the Chinese have kept a prudent distance between the two countries. They have emphatically conveyed that, far from allying themselves with the US, they are pursuing an independent and nonaligned policy.
The Chinese have been careful to avoid any appearance of a strategic alignment with the US against the Soviet Union. They in fact announced on the eve of the Reagan trip that Ivan V. Arkhipov, a Soviet first deputy prime minister, would visit China in May for talks on expanding Sino-Soviet trade and technical cooperation.
While major conflicts will exist in Sino-Soviet relations, the two communist nations are trying to improve ties. To avoid offending the Soviets while these efforts are under way, the Chinese, in broadcasting the taped speech given by Reagan to several hundred Chinese scientists and intellectuals, deleted references to the Soviet troop buildup on the Chinese border and the shooting down of a South Korean airliner. A US official characterized the deletion as ''regrettable'' but suggested that the Chinese ''did not want to offend a third country.''
They also did not let Mr. Reagan say everything he wanted to the Chinese people. In the same address, the President extolled the virtues of democracy and capitalism. These portions and a reference to God were deleted.
Assessing the visit, which ends Tuesday, US officials tend to dwell on the areas of agreement and on hopes for future cooperation. Chinese officials, in briefing reporters, have stressed the differences on a wide range of issues. They make the point that the Sino-American relationship is just ''sprouting'' and needs careful nurturing.
Taiwan is the knottiest problem in relations. ''The question of Taiwan remains a major obstacle to stable, sustained development of Sino-US relations, '' Zhao told US reporters. The Chinese voiced concern about a proposed resolution in the US Congress calling for the future of Taiwan to be decided by the people there, a move seen as support for an independent Taiwan.
US officials say President Reagan pledged that he would abide by the August 1982 communique calling for a reduction in US arms sales to Taiwan and would also oppose any efforts to upgrade US ties with Taiwan.
Technology transfers are the second major area of concern to China. The two sides were able to announce the conclusion of an agreement on nuclear cooperation. But the Chinese objected to US legislation that prevents sales of some sophisticated equipment to China, terming such legislation ''discriminatory.''
In response, the President cited substantial progress in technology transfers so far and pledged that efforts to loosen export controls would continue, officials say.
The Chinese noted other positions at variance:
* They criticized medium-range missile deployments in Europe by both the Soviet Union and the US and urged a resumption of arms negotiations.
* They voiced objection to ''meddling'' by any big power in Central America, criticized the mining of Nicaraguan harbors, and urged the US to back the Contadora group's efforts toward a negotiated settlement.
* They suggested the US should negotiate with Yasser Arafat and the Palestine Liberation Organization.
* They said they were ''not in favor'' of the stationing of US troops in South Korea and backed North Korea's proposal for tripartite talks on reunification.
The US emphasized that the interests the US and China have in common are ''far more important'' than their differences. Mr. Reagan reportedly reaffirmed a desire for arms talks, pointed to steps that could reduce tensions on the Korean peninsula and backed four-power talks including China, and said that the Central American problem is caused by Soviet arms.