With the British government suffering a political thrashing anew and the Irish government only now sorting out its own internal tumult, many analysts here are saying the already difficult search for peace in Northern Ireland may get even more complicated.

Prime Minister John Major's British government suffered its latest disastrous defeat Thursday.It lost a "safe" Conservative seat in Parliament in a by-election to the surging Labor Party which, under its new leader, Tony Blair, is running far ahead of the Tories in polls.

In balloting in wealthy Dudley West, in the Midlands of England, Labor won by a whopping 20,694 votes - the worst by-election drubbing for the Conservatives since World War II.

The Tory defeat was particularly painful because only 7,706 people voted for the ruling party, compared with 34,729 in the April 1992 election.

Labor's vote held steady at 28,400.

If translated into national terms, the voting this week would leave the Conservative Party without a single parliamentary seat.

And the dire election results raised serious questions as to whether Major can effectively govern in the two-plus years his administration still has to run.

Meanwhile, in Dublin, a new government finally has been cobbled together with a coalition led by newly installed Premier John Bruton, leader of the Fine Gael Party, replacing the Finna Fail administration of Premier Albert Reynolds.

Reynolds had led the Anglo-Irish move for talks with the maverick Sinn Fein, the political arm of the Irish Republican Army, and extremist Protestant paramilitary groups in Northern Ireland.

While Bruton's Fine Gael has fewer ties with Sinn Fein and often has viewed the group as an anti-democratic force, he has promised to continue the peace process launched by Reynolds and Major; on Friday, Bruton met Sinn Fein president Gerry Adams and leading Northern Irish militant Republicans.

But even as the quest to end 25 years of violence continued, there were signs of just how tangled the peace process may become:

- On the one hand, in what was viewed as an encouraging development, Bruton re-appointed Dick Spring, head of the Labor Party, as Ireland's foreign secretary. Spring held that post under Reynolds and used it to promote peace talks on Northern Ireland.

- Without firm direction from London, though, the 900,000 Protestant Unionist majority in Northern Ireland has indicated it may be loath to reach any agreements with the 600,000 Catholic minority.