One is that Mr Tudjman resolve in a democratic manner the crisis he sparked by riding roughshod over the elected members of Zagreb's local council, controlled by the opposition. Having rejected several council candidates for mayor, the President decided to wash his hands by dissolving the assembly and appointing a single commissioner in its place. He did the same in Rijeka, where the county council was proving a little troublesome.
How Mr Tudjman will come up with a "democratic" solution is something of a mystery, given his utter refusal to accept defeat in Zagreb. "Tudjman lost the elections - that's the key problem for him, and he has not the honesty to admit that he lost," said Davor Gjenero, a political analyst.
Mr Gjenero fears that the radical faction within the ruling Croatian Democratic Union (HDZ) - that is, the more nationalist, right-wing element, many of whom are in fact Bosnian Croats from Herzegovina - will encourage the President towards totalitarianism.
"The biggest problem nowadays is whether Tudjman will transform his system into a full-blown dictatorship," Mr Gjenero said. "He has the power . . . and he is capable of doing it, as his actions in Zagreb and Rijeka have shown." In theory, Croatia must fulfil the conditions laid down by the Council of Europe, which include democracy, freedom of the press and the judiciary, respect for human rights and minorities.
The omens, however, are not good. Since Croatian entry was approved by the permanent representatives last month, the government appears to have geared up its campaign against the independent media and other opponents.
One newspaper has been closed (for violating technical and environmental laws) and a second hit with fines that could bankrupt it (on bizarre tax charges), while the editor of a satirical weekly has been charged with insulting the President (under a new defamation law).
There are other subtle forms of attack. A prominent human rights campaigner, Ivan Zvonimir Cicak, was splashed across the front of the pro-government daily Vjesnik, accused of working for the Yugoslav secret police since the age of 16. The charges appear to be completely unfounded, local analysts say; for one thing, Mr Cicak was jailed and harassed regularly by the Yugoslav authorities.
Journalists outside Panorama, Novi List and Feral Tribune - the most recent media victims - are eyeing their backs nervously, wondering when they will be called in for an "informal chat" with officials. Novi List is planning to fight the tax charges in court; but few analysts here have much faith in the judiciary.
"The legal system in Croatia in 1990 was in an awful condition and now it is worse," Mr Gjenero said flatly. The parliament - controlled by the HDZ - appoints the committee that in turn appoints judges for life, a system of patronage that provoked the resignation last year of the justice minister.
Television and most radio stations are under the total control of the HDZ, which runs the three state channels.During elections, the nightly news becomes a lengthy HDZ campaign advertisement.
But with the business of Croatia's five-year conflict mostly finished, ordinary people have begun to question Mr Tudjman's rule. The HDZ, which came to power on a platform of Croatian nationalism and independence, is on a downward slide. Without the fig-leaf of war with the Serbs, it has been exposed as corrupt and inept - hence the need to crack down on the media.
The HDZ radicals, Mr Gjenero said, do not want closer ties to Europe, for good financial reasons. "They are very isolationist, and it would not serve their economic interests," he said. "If Croatia really becomes part of the economic process, if it has open markets and a democratic system, the economic monopolies created over the past three or four years will collapse."
This, of course, is the hope of those supporting Croatian entry. "There is no problem with the principle of Croatia joining the Council of Europe. The debate is one of timing," said a Western diplomat in Zagreb. "There are those saying, look, Croatia is moving in the right direction, we should take them in now." That, he added, is the position of the opposition here.
But Mr Tudjman shows few inclinations towards "European" values. He assures horrified diplomats that wholesome, Catholic Croatia, will act to keep the filthy Serbs and Muslims out of "Europe".
"It grates," admitted the diplomat, of Croatia's admission to the Council.
Leading article, page 14