The challenge comes from two of Croatia's most prominent and experienced politicians, Stipe Mesic and Josip Manolic, who respectively lead the lower and upper houses of parliament.
The two men were once leading lights in Mr Tudjman's ruling party, the Croatian Democratic Union (HDZ). Last month they broke away and formed a new party, the Croatian Independent Democrats (HND). Mr Tudjman will try this week to persuade parliament to strip the two men of their posts.
If he fails, it will indicate that Croatian political opinion is finally turning against the President and his HDZ cronies, after four years.
The rebels argue that Mr Tudjman has not turned the first truly independent state in Croatia's history into a liberal democracy.
Instead, they say, he has persecuted political opponents, suppressed the independent media, created a new oligarchy of HDZ loyalists, many of whom are former Communists, pursued fatally misguided policies in Bosnia, and in general tarnished Croatia's international image. 'Fear is now reigning in Croatia,' Mr Mesic and Mr Manolic said, in a statement that described the country's internal politics as close to 'an abyss of one- party totalitarianism'.
They added: 'If decisions in parliament and the HDZ were passed in a secret ballot, the real proportion of opposition to the authoritarian and anti-democratic policy of a part of the present HDZ leadership would be seen. Let us not allow fear and dangerous silence to spread across Croatia, as the present HDZ leadership needs this to impose an authoritarian personal regime.'
Mr Tudjman has twice won elections to Croatia's presidency. He remains popular with hundreds of thousands of people, who see him as the father of Croatian independence. At the same time, opinion polls show a consistent fall in support for the HDZ. Many voters are transferring their allegiance to the centrist Croatian Social Liberal Party and regional movements in Istria and Dalmatia.
Mr Tudjman's HDZ allies exercise total control over state television. By last year they had suppressed virtually all anti-government comment in Croatian newspapers. However, in a sign of possible change, some parts of the press have given space to the Mesic- Manolic rebellion.
The two men have savaged Mr Tudjman for colluding with Serbia's President, Slobodan Milosevic, in the attempted partition of Bosnia-Herzegovina.
They have pointed out that as long as Croatia is seen as willing to break up a neighbouring state, it will win little international sympathy for its efforts to reclaim the 30 per cent of Croatian territory that was lost to Belgrade-backed Serbian rebels in the war of 1991.
They also say that the Croatian war against the Muslims not only alienated the West, but went badly wrong, in that it almost resulted in the destruction of historic Croatian communities in central Bosnia.
However, Mr Mesic and Mr Manolic may have launched their political revolt too late. Under heavy American pressure, Mr Tudjman recently ended the war with the Muslims. He also forced the dismissal of Mate Boban, the radical nationalist who had established a secessionist Croatian mini- state in Bosnia.
The so-called 'Herzegovinian lobby', who favour Croatia's territorial expansion into large parts of Bosnia, appear to have lost ground to moderates, who support an alliance with the Muslims. However, the influence of rich Herzegovinian expatriates from the West, who have bankrolled Mr Tudjman's state and secured jobs in his government, has not completely disappeared.
Opposition politicians detect weaknesses in the Mesic-Manolic campaign. Ivan Bozicevic, of the Social Liberal Party, said: 'They rely on the relative political weight that comes from the image of being HDZ dissidents. This is a position of luxury and comfort, but it lacks political perspective.'
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