Zbigniew Brzezinski went to Peking determined to allay Chinese concerns about American policy. The president's special adviser on national security seems to have enjoyed great success.

Still there will be no immediate payoff in actions that inhibit Russia's assertive policies. Which shows that even the best thing the United States has going in international affairs - the quasi-alliance with China - has not evolved in a way that makes it easy to check Russia's present course.

Brzezinski's overtures to China took three forms. First and most important, he stated in the strongest terms American determination to stand up to the Soviet Union around the world. He spoke of the "common interest" between the United States and China in containing Soviet expansion. He indicated the interest was "strategic" and "long term," not merely for some tactical advantage.

He used language very similar to the language used by the Chinese themselves in denouncing some of the Cubans in Africa as "marauders masquerading as non-aligned."

Second, Brzezinski associated the United States with the modernization drive of the current Chinese regime. He indicated the United States was prepared to help China in economic and technological development. He asserted - for the first time in a long time, I think - the U.S. interest in a "strong China."

Finally, Brzezinzki was more forth-coming than any previous spokesman for the Carter administration on the issue of resuming diplomatic relations with Peking. He moved beyond the see-saw debate on how to balance off progress with mainland China against commitments to Taiwan. He seemed to brush away the threat of right-wing opposition to a break with Taiwan that would be necessitated by resumption of diplomatic ties with Peking. He said: "The United States has made up its mind" to move toward normalization with mainland China.

No doubt those comments did not allay all the Chinese doubts and misgivings about American policy. The United States has not matched the Soviet military buildup, and it has seemed to yield to pressure in Africa and other places. Six years have passed since the Shanghai Comunique seemed to promise normalization to Peking. So the Chinese have reason to worry, and they undoubtedly expressed their concerns in what Peking has called "frank" and "candid" talks.

On the other hand, Brzezinski gave the Chinese far more of what they wanted than they have ever received previously from the Carter administration. So there is every reason to believe that the talks were what the Chinese called "useful," "constructive" and "beneficial."

The more so as the Chinese were obviously in the mood to hit out at the Russians and align themselves with the United States. Thus earlier this month the Chinese made a point of singling out for wide publicity a minor Soviet border incursion. Even as Brzezinski was visiting Peking, the revered former defense minister Yeh Chien-ying met in a highly emotional ceremony with a group of former U.S. Army men to celebrate the high tide of U.S. cooperation with the Chinese communists during World War II.

So there is no doubt that Sino-American ties are solid, and there is shaping up more cooperation - particularly in the economic field. What is missing is a quick dividend in terms of the three-cornered relationship among Washington, Peking and Moscow.

The United States does not emerge from the Brzezinski mission to Peking in better position to deter the Soviet advances in Africa, nor to wring more favorable terms from Russia in the arms-control negotiations. China is not strong enough to exert serious pressure on Russia for more careful behavior anywhere in the world. Nor, despite American help, will China achieve that kind of strength for years to come.

The fact is that the magic is now out of the three-cornered relation. The concessions exacted from Russia by President Nixon and Henry Kissinger under the threat of some kind of Sino-American deal are at an end. The Chinese card has been turned up, and it is not a trump. So Brzezinski's success in Peking only reinforces the lesson that the building of barriers against Soviet assertiveness is a long, hard, slogging job.