Both houses of Congress adopted similar bills yesterday that establish a new basis for U.S. relations with Taiwan while asserting contiuning American interest in Taiwan's de facto independence from China.

The Senate vote was 90 to 6, the House vote 345 to 55.

Happy Carter administration officials regarede these big majorities in the House and Senate as victories for the president and his policy of normalization of relations with Peking. But key members of Congress could point to important changes in the administration's original legislation that toughened it appreciably.

Specifically, Congress went much further in its assertion of American interest in Taiwan's future now that the United States has recognized the Peking alaim to sovereignty over Taiwan's 17 million people.

The Carter administration stated unilaterally in its negotiations with Peking that it expected a peaceful resolution of the Taiwan question. Congress went much further, declaring as a matter of law that the United States will maintain "extensive, close and friendly relations" with Taiwan, will maintain a military capacity to resist any threat to Taiwan or its social and economic system, and will consider any threat to Taiwan from Peking a threat to the security of the western Pacific and "of grave concern to the United States."

These positions enjoyed strong bipartisan support in both houses. Attempts to make them even stronger were defeated in both, as were numerous amendments offered by Republican conservatives who sought to give an official character to future American -Taiwanese relations.

Underthe bills passed yesterday, Congress has accepted the administration proposal to establish a new "unofficial" basis for relations with Taiwan. Under this formula, the two entities -- Taiwan is no longer regarded as a country -- will conduct relations through institutes or offices that are theoretically separate from their governments.

In fact, these bodies will be staffed by government employes on both sides. These employes will take fictional leaves of absence from their government posts while workeng for the "unofficial" offices.

The last day of debate in both houses was anticlimactic. A strong consensus had formed around the basic proposals, and attempts by frustrated conservatives to alter them came to naught.

The two versions are not identical, and will have to be reconciled be reconciled by a conference committee. Their major provisions are the same, however, and a speedy agreement is expected.

Until a fimal version of the measure is passed by both houses, the United States will have no office in Taiwan representing American interests or helping American citizens there. A Senate Appropriations subcommittee chaired by Sen. Ernest F. Hollings (D- S.C.) responsible for State Department funds to finance the "American Institute on Taiwan," and the old U.S. embassy there closed March 1.

A spokesman for Hollings said last night he will wait to see the final version of the bill before moving on the request for money.

Apart from the statements on Taiwan's security, the House and Senate bills contain two relatively minor provisions that the administration had opposed. One grants permanent ownership of the old Taiwanese Embassy in Washington to Taiwan, despite the administration's stated belief that it rightly belongs to China. The second is a provision creationg a congressional commission to oversee the activities of the "American Institute on Taiwan" to be sure it meets Congress' stated objectives for U.S.-Taiwanese relations.

Sen. Frank Church (D-Idaho), chairman of the Foreign Relations Committee and the key architect of the Taiwan security language, praised the Senate bill last night, saying it "does away with the charge that the United States walked away from an old ally to do business with China."

Administration officials acknowledged yesterday that their own China Experts originally predicted that Peking would not tolerate action by Congress asserting U.S. concern for Taiwan's security, but the experts later decided this was going to be acceptable after all.

The Chinese ambassabor in Washomgton, Chai Zemin, has expressed "grave concern" to Secretary of State Cyrus R. Vance over the Taiwan security lauguage, but there has been no threat to reject it or to allow it to interrupt normalization of Sino-American relations.