No breakthroughs are expected to occur when China's Premier Zhao Ziyang visits here this week, but his visit is nonetheless viewed as highly important. The fact that the visit is taking place at all after a delay and then some further hesitation on the part of the Chinese may turn out to be the most significant thing about Zhao's talks here. The top Chinese official's visit symbolizes the progress which the two nations have made over the past year and a half in strengthening ties.
American experts who favor a stronger US-China relationship are pleased that Premier Zhao seems to be soft-pedaling the contentious Taiwan issue for now. Both sides appear to have grown more sensitive to - or at least knowledgeable about - the other's domestic political difficulties in dealing with this problem.
One expert, political scientist Kenneth Lieberthal of the University of Michigan, argues that there is now an ''underlying stability'' to US-China relations. But he adds that the ''atmospherics'' of the relationship are still volatile, with the decentralized American system of power always capable of generating insults to the Chinese on certain questions, including the Taiwan issue.
The National Council for US-China Trade, a private, nonprofit organization established in Washington to promote bilateral trade, issued a statement Jan. 6 saying that the Council is optimistic about the further improvement in relations and the expansion of trade.
''In the past year and a half, we have seen resolution of the major issues confronting the relationship, and though irritants and problems remain, they strike us as manageable,'' said the Council's president, Christopher H. Phillips.
''The US-China political relationship, after a disturbing two-year period of unfortunate rhetoric and mutual misunderstanding, is back on track,'' said Phillips.
The Reagan administration got off to a rocky start with Peking after President Reagan came to office in 1981. The Chinese were highly mistrustful of Reagan because of his election campaign statements concerning a possible strengthening of ties with Taiwan and his criticisms of earlier administrations's moves to establish relations with China. The biggest conflict of all has been over continuing American arms sales to Taiwan.
According to Mr. Phillips, the Taiwan issue took ''center stage'' in 1982 and threatened to disrupt relations. But, says Phillips, the issue was ''deftly handled'' in US-China negotiations, culminating in a joint communique issued on Aug. 17, 1982.
Under that agreement, the Reagan administration stated that the US does not seek to carry out a long-term policy of arms sales to Taiwan and that such sales will not exceed, either in qualitative or in quantitative terms, the level set since the establishment of diplomatic relations between the US and China. The administration also stated that the US intends to ''reduce gradually'' such sales, leading over a period of time to a final resolution of the issue.
At a press conference in Peking, shortly before his departure for the US, Premier Zhao Ziyang said he would not ask President Reagan or other officials for any immediate cutoff of US arms sales to Taiwan. He said China will be satisfied if the US adheres to its pledge to reduce sales gradually.
The other major issue between the two nations, that of US controls on high-technology exports to China, was to a great extent resolved in May 1983, during a trip to Peking by Commerce Secretary Malcolm Baldrige.
Mr. Baldrige informed the Chinese of a decision by the Reagan administration to place China in the category of friendly, nonallied countries for the purpose of increasing such exports.
This set the stage for an increased US role in the development of China's computers and telecommunications, offshore oil reserves, and coal and hydroelectric power industries. Following difficult negotiations, a US-China textile agreement was also concluded last year.
During the Zhao visit to Washington, no major agreements are expected to be announced. But Zhao is expected to initial a new industrial and technological cooperation agreement. Negotiating progress has also been made toward new US-China treaties on taxes and investments. A US official said last week in a briefing for reporters that the investment treaty, which would be required for any significant increase in private American investment in China, could ''theoretically'' be ready for signing during President Reagan's visit to China next April.
A new agreement on peaceful uses of nuclear energy is also reported to be in the final stages of negotiation. US officials say that the delay in the signing of such an agreement has been due to differences over the strictness of nonproliferation safeguards which would apply to China. A US official said that China's decision to join the International Atomic Energy Agency was an important step toward providing safeguards.