LONDON, JUNE 16 -- Less than a week after its poor showing in the general election here, Britain's two-headed Alliance is suffering an identity crisis that is likely to end in its breakup or its emergence as a single political entity.

The question of a merger between the Liberal and Social Democratic parties has hovered in the background since they joined in an electoral coalition six years ago. Long favored by Liberal leader David Steel, a merger has been strongly opposed by his Social Democratic counterpart, David Owen.

But in the wake of Prime Minister Margaret Thatcher's landslide victory Thursday, the Alliance and the leading opposition Labor Party are expected to undergo major reevaluations of their organization and strategy.

The question has been most acute for the Alliance, which had told voters that this election was "the last chance" to choose a middle way between the left-right extremes of Labor and Thatcher's Conservatives. When the votes were counted, however, the Alliance share had fallen from 25 percent and 27 Parliamentary seats to 22 percent and 22 seats.

To Steel, who long had argued against the dual party leadership as confusing and unappealing to voters, the electoral results pointed to only one course of action -- a "fusion" between the two parties under one still-to-be-decided leader.

Over the weekend, he called for merger by the end of this year and the formation of a new party called the "Liberal Democratic Alliance" that would challenge Labor as an "effective center-left movement" and compete directly with Thatcher's Conservatives the next time around. The announcement brought no response from Owen.

Yesterday, the 26-member national committee of the Social Democratic Party (SDP) met in London to consider Steel's proposal. The committee announced that it had postponed a reply for two weeks, pending further consultations.

Owen made no comment to waiting reporters as he emerged from the meeting, but SDP President Shirley Williams said the committee had been "pretty split" over the merger issue. "Resentment is too strong a word to use," Williams said. "But there was a feeling that the members were somewhat being bounced" into a takeover by the larger Liberal group.

Today, Steel stepped up the pressure, publicly releasing a memorandum on the subject. Outlining three alternatives for the future, Steel said the Alliance could remain as it is -- two separate parties with separate membership and policy-making apparatus, joined together at election time to present a joint slate of candidates and a melded platform.

The second alternative, Steel said, was for the Alliance to break up altogether, with the Liberals and the SDP going their separate ways. That prospect is likely to send both parties into political oblivion.

Steel said he would prefer a third alternative, "the formation of a single organization, a Liberal Democratic Alliance, incorporating the best aspects of both our existing parties."