Gloomy patriotic music fills the state-run broadcasting services, heightening the atmosphere of uncertainty in Zagreb's Habsburg-era streets and squares.
Although the 77-year-old president has been reported to be suffering from cancer since late 1996, this has never been officially confirmed, and a succession of bulletins from his doctors have heightened rather than dispelled speculation. Some people in the capital are willing to believe that he may already have died, and that the leadership is suppressing the news in the manner of the old Kremlin.
Doctors reported yesterday that the president was still in intensive care and that there were further complications with his digestive system. His health took a serious turn for the worse last week after urgent abdominal surgery was complicated by peritonitis.
President Tudjman's illness comes at a critical time: parliamentary elections are tentatively scheduled - though not yet formally called - for 22 December, but on Friday his deteriorating health prompted the ruling party to withdraw a motion to dissolve parliament. Its mandate formally expires on 27 November.
If Mr Tudjman dies, the parliamentary speaker, Vlatko Pavletic, would act as interim president for up to 60 days, in which time a presidential election must be held. But there is no one of equal stature to inherit his position. More than anyone else, Franjo Tudjman is the architect of this former Yugoslav state, which broke away from Belgrade's unwelcome embrace in the bloody and prolonged 1991 war of independence. Although Croatia is a parliamentary democracy - and the only ethnically homogenous state in the Balkans - he has shaped foreign and domestic policy in the classic tradition of a Balkan strongman.
Mr Tudjman has played a delicate balancing act, deflecting increasing criticism from the West of Croatia's human rights record with the knowledge that he is needed as a counterpoint to his neighbour, Slobodan Milosevic, the Yugoslav president.
The country is deeply divided over Croatia's future direction, and many expect that his party, the ruling Croatian Democratic Union, will lose power in the parliamentary elections scheduled for December. But there is no doubting Mr Tudjman's achievements in making a new country out of the wreckage of the old.
When he came to power in 1991, Zagreb was a city at war. Pedestrians frequently ran for cover as Yugoslav jets flew over; shop windows were taped to prevent flying glass and the boom of shelling echoed around the streets.
Now the city, like its neighbouring capitals, Budapest and Lubljana, is a modern mini metropolis with stylish cafes, fashionable shops and the feel more of Europe than the Balkans.
But, despite his repeated assertions of his democratic credentials, many see President Tudjman as a figure who has more in common with Mr Milosevic, his deadly rival and accomplice in the dismemberment of Bosnia. Mr Tudjman, a former Partisan general, found it hard to break free of his political training in the Tito era.
During the early 1990s, Croatia came under heavy diplomatic pressure over its role in Bosnia with the Bosnian Croat army, the HVO, engaged in large-scale ethnic cleansing using similar methods to the Bosnian Serbs. But President Tudjman has always been bolstered by his close ties with the US; Washington regards Croatia as an essential ally in the continuing struggle with Serbia.
Already the battle for succession has begun. "The main question for Croatia is to know who is currently running the country," the daily independent newspaper Jutarnji List wrote recently.