Vice Minister Teng Hsiao-ping, tired and ailing at the end of his eight-day U.S. tour, declared himself fully satisfied with his new international connection and said normalization of Sino-American relations opens the prospects for "extensive cooperation."

At an airport departure ceremony, moved inside because of rain and Teng's sniffles and fever, the Chinese leader took a parting shot at the Soviet Union.

Noting that the United States and China in several communiques agreed on opposition to hegemony, China's code word for Soviet domination, Teng declared, "The Chinese people will do their bit toward opposing global and regional hegemonism." No details were given of how they will "do their bit" (or "use their efforts," in a more literal translation from the Chinese).

The immediate question mark was action against the southern neighbor, Vietnam, which is accused by China of being a Soviet-led "regional hegemonist." China has recently massed 10 to 12 divisions and more than 150 warplanes near the Sino-Vietnamese border.

Foreign minister Huang Hua, who substituted for the ailing Teng at a breakfast meeting with editors and reporters, charged Vietnam with naked aggression in Cambodia and said peace-loving nations should not sit idly by and do nothing.

An American official who participated in last week's White House talks said Teng never disclosed what China plans to do with the extensive troop buildup.Reporting that Teng told members of Congress that Vietnam must be "taught a lesson" and that "the lesson has to come," the official said he personally would not be surprised if China takes military action.

A punitive raid with large forces rather than an attempt at conquest is considered to be the most likely course if action is taken. There is much speculation and concern in official circles about a potential Soviet counterstrike in the event of such military action.

The official U.S. position has been to call for Vietnamese withdrawal from Cambodia and to urge restraint on China, Vietnam and the Soviet Union lest the Indochina conflict spread through Asia. However, Teng's net impression of U.S. attitudes may be different. Some members of Congress made clear that they have little sympathy for Vietnam. "Nobody stopped Japan in 1931" (when it invaded China), one lawmaker reportedly remarked to Teng.

Both U.S. and Chinese officials, interviewed in Washington and during the Teng road show, said the principal objective of Teng's journey was to establish and symbolize the new Sino-American relationship. Both sides expressed the belief that this objective had been effectively accomplished.

A senior Chinese official said it had been "very important" that Teng personally took part along with President Carter in laying the new Sino-American foundations, evidently because leadership commitments from the top can cut through many difficulties.

Sino-American agreements on science and technology, cultural exchange and consular affairs were signed in Washington during the trip. U.S. sources said statements by Teng in White House meetings made it likely that the 30-year-old problem of Chinese and American claims and assets can be solved during the Peking trip of Treasury W. Michael Blumenthal later this month.

A liberal Chinese attitude on emigration policy, which is tied to trade benefits of communist nations by the Jackson-Vanik Amendment, was reaffirmed today by foreign minister Hua. He said China is ready to take effective measures to permit its people to emigrate to reunite families, but that obstacles had been encountered from the United States and other nations, which are reluctant to accept new Chinese residents.

Teng told Carter in Washington, perhaps in jest, that China is willing to send out 10 million or so of its vast population whenever the United States is ready. In greater seriousness, the Chinese leader reported that Hong Kong has appealed to Peking to limit the outflow of its population so as not to swamp the colony.

Teng said at every stop on his tour that China is interested in trade with the United States in the interest of modernization, and American political leaders as well as businessmen made clear their eagerness to participate in the new market.

Although several hundred pro-Taiwan demonstrators -- nearly all of them of Chinese origin -- paraded against Teng at every stop on his tour, remarkably little was said to or by the Chinese leader about the Taiwan issue.

Summing up his trip throughout the country. Teng in the departure ceremony said he had seen "beautiful landscapes, a rich land a developed economy." He called gestures of friendship displayed by the American people "unforgettable and expressed hope that Americans from all walks of life will visit China in return.

Then the 74 year-old Chinese communist leader, who said in November that he wished to see the United States before he "meets Marx" in another life, was helped by an aide up the ramp of the Chinese commercial airliner. He waved his hand and applauded his applauders briefly, as he did many times during his U.S. tour. Then the plane took off for Japan, where Teng plans to stop for two days before going home.