China's invasion of Vietnam strained its relations with the United States, Japan and Western Europe, but the early indications are that China's prestige has been enhanced among the non-Communist nations of Southeast Asia.

In public, no national leaders have applauded the invasion, but there are private indications that Asians have been impressed and not displeased by Peking's effort "to teach Vietnam a lesson."

Since the collapse of the American-supported governments in Cambodia and South Vietnam in 1975, Vietnam moved closer to the Soviet Union while extending its control over Laos and, last January, conquering Cambodia.

China's invasion, several observers here say, demonstrated that the Vietnamese with Moscow behind them cannot act with impunity and will alter the trend of events in the Southeast

Most immediately, there is likely to be greater relaxation in the ASEAN nations -- Thailand, Malaysia, Singapore, Indonesia and the Philippines -- because Vietnam's ability to act with a free hand has been impaired.

While much of the world denounces China for its beligerence and praises the Soviet Union for reacting with moderation, the Southeast Asian view, at least at this early stage, seems to be that China comes away with its reputation enhanced because it proved it could show its muscle without suffering retaliation and the Soviets were found to be "paper bears."

ASEAN nations had been skeptical of China's willingness to act militarily. Now, observers believe, China has changed the Asian geopolitical balance.

Although its invasion was limited in time and space, when China takes its troops home it doesn't take them to bases thousands of miles away. They remain on Vietnam's northern border.

Thailand, the only ASEAN nation that borders Indochina, has the most to gain from a new power alignment that inhibits Vietnam.

The thais have been moving closer to China in recent years and have made clear their willingness for contiued improvement of relations.

Malaysia and Singapore traditionally have been suspicious of China and their reactions to the invasion are more mixed, according to informed sources. An expansionist China possibly meddling in their Chinese communities would be a serious threat, but they are not displeased at the comparison between warring Communist nations and the generally good relations forged by ASEAN over the years since the U.S. defeat in Indochina.

Singapore Foreign Minister Sinnathambly Rajaratnam said Tuesday that ASEAN has cooperated peacefully while Vietnam has sought to create an Indochina confederation "by way of occupation armies."

In a reflection of the lack of dismay around the region over the invasion, Rajaratnam said "the practitioners of communism are really xenophobic nationalists fighting, like the capitalists of old, for national glory, national aggrandizement and loot."

Only in Indonesia among the ASEAN nations did China perhaps set back its efforts to gain influence in the region. Indonesia is still suspicious of China's potential to make trouble in the nation's large Chinese community as it did during the Sukarno years and there are indications that the invasion may have pushed back the timetable for a renewal of Indonesian-Chinese ties.

The long-term effects of China's resort to military force will depend on how China, Vietnam and, to a lesser extent, the Soviet Union, maneuver after the Chinese troops have completed their withdrawal.

The Chinese-Vietnamese negotiations are likely to be extremely prolonged and each side will watch carefully for new border incidents of the sort that preceded the invasion.

The border regions are populated largely by hill tribes on both sides. The ttribes have traded back and forth across the frontier and Vietnam has accused China of using some of these people as guides and saboteurs during the recent fighting. The potential for continued infiltration remains a temptation.

ASEAN nations, particularly, Thailand, also will be watching closely what happens in Cambodia. Although Chinese leaders said one of their invasion's objectives was to force Vietnam out of Cambodia, Vietnam did not pull any significant military units out of Cambodia where it is fighting against guerrillas of the Khmer Rouge whom China supports.

For the Soviet Union, the apparent lesson of the Chinese invasion is that Moscow cannot de much to help its Vietnamese ally short of taking military action on the Sino-Soviet border.

A Soviet military presence in Vietnam could dramatically enlarge Soviet options and there has been speculation that Moscow may now move to establish itself with the former American base Cam Ranh Bay.

The conflict between China and Vietnam is likely to go on for a long time. One of the lessons China would like to teach the Communists neighbor is that Hanoi makes a mistake by relying so heavily on the Soviet Union.

Information about Vietnam's policy debates is extremely closely held in Hanoi, but analysts believe that there was a purge of pro-China figures during 1977, although it did not affect any of the top leaders.

China's invasion could well harden Hanoi's determination to keep to its present course, but the invasion seems likely to be only the beginning of a long Chinese effort to influence Hanoi's future policies in an effort to create a more friendly state on its southern border and weaken Soviet power there.