Senior political commentators fear the allegations could engulf Spain's political leadership in the kind of scandal which has swept through Italian politics.
Mr Gonzalez insists that he will continue until the end of his term in mid-1996, but the political row over his alleged involvement in anti-Basque separatist death squads during the early years of his premiership forced him this weekend to make overturesto the opposition conservative Popular Party. The leader of the PP, Jose Maria Aznar, says he is not interested in talks unless they deal with the calling of elections which he would like brought forward to May.
A poll at the weekend showed that 52 per cent of Spaniards would favour such a course.
The Socialist Party, which holds power in coalition with the Catalan nationalists led by Jordi Pujol, may be forced to consider replacing Mr Gonzalez as prime minister. But there is no obvious successor - a measure of how discredited is the entire Socialist leadership.
The Socialists have challenged Mr Aznar to put a motion of censure before parliament when it reconvenes in February. But the conservative leader is reluctant to do so until he is sure of winning the vote.
To this end he is seeking new allies, including - bizarrely for a party founded by old Francoists - the United Left, an amalgam of former Communists and disaffected left-wing socialists led by Julio Anguita.
Mr Gonzalez's government, now in its third term, has in the last 18 months been beset by a succession of scandals. Bereft of new ideas and new faces, it has shown no will to deal with the mounting problems.
The affairof the GAL death squads, however, in which the Socialist former Interior Minister, Jose Barrionuevo, is implicated, is the one most likely to bring the government down.
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