The Barbalics are ethnic Croats. The mayor of Zemun, as of last November, is Vojislav Seselj, leader of the ultranationalist Serb Radical Party, who likes to brand all Croats as Ustasha, or crypto-Nazis, and has decided to indulge in a little "ethnic cleansing" on his doorstep.
So appalled were the Barbalics that they went away for a few days' holiday. When they returned, the locks on their apartment had been changed, their belongings had disappeared, and their home had been taken over by Liljana Mijovic, wife of the editor of Mr Seselj's local party paper.
They took the case to Belgrade District Court, which ruled in their favour. But, more than two weeks later, they still have not been able to re-enter their home because the police have refused to enforce the eviction order.
The Barbalics are not alone. Several Croat families in Zemun have returned from holiday in the past month to find their homes occupied by ethnic Serbs, many of them refugees from Croatia, who have been told by Mr Seselj that the flats are public property, his to dispose of as he sees fit. One man, Petar Gojcevic, was only out for a walk when the expropriators swooped.
Such behaviour was one of Mr Seselj's hallmarks during the Yugoslav wars of secession, when he regularly incited inter-ethnic hatred, for example urging Serbs to scoop out Muslims' eyes with spoons. In 1991 and 1992, he drew up lists of properties occupied by Muslims and Croats in Vojvodina, the semi-autonomous farming region in northern Serbia, and openly invited Serb refugees to steal their houses.
But the war is over, Serb nationalism has been largely given up as a lost cause, and Zemun is the sort of community where things like this are not supposed to happen. And yet they do.
A week ago, Mr Seselj was invited on to a television programme with the Barbalics' lawyer, Nikola Barolic. Within minutes, the Radical Party leader was insulting Mr Barolic's dead father. Mr Barolic said Mr Seselj's wife was a whore, and threw a glass of water into his face.
"You can't provoke me here in a studio, whatever you do," Mr Seselj shouted as the programme was brought to a halt, "but you will pay a very high price for this." It was no idle threat. Minutes later, as Mr Barolic was recovering in the editor's office, one of Mr Seselj's bodyguards stole up behind him, kicked him in the head and pummelled him with punches.
After a while, Mr Barolic heard Mr Seselj say: "That's enough, we can go." He was left writhing on the floor with a bruised and bloodied face, a nose broken in three places and a cracked rib. More than a week later, he is still in hospital and has just undergone surgery to help him breath through his nose.
One of the most striking aspects is the impunity with which Mr Seselj has acted. Nobody has sought to prosecute him for the violence; despite plenty of witness evidence to the contrary, he insists Mr Barolic "slipped on a banana peel". The bodyguard, Petar Panic, has a licensed firearm even though he has been prosecuted for two murders and a slew of grenade attacks.
The old suspicion that Mr Seselj is acting on behalf of his on-again, off-again mentor Slobodan Milosevic, is growing. "We are concentrating on tying Seselj to Milosevic because the one is the bastard son of the other, following his instructions transparently and explicitly," said Miodrag Perisic, deputy leader of the opposition Democratic Party.
The events have alarmed ordinary Belgraders, who lost much of their fear of Mr Milosevic's regime over the winter when they marched in the streets for three months to demand democratic reforms. There have been demonstrations outside the Barbalics' house every day for three weeks, and others outside the Zemun municipal building. A group of civil rights groups have launched an anti-Seselj campaign, demanding he be pushed out of politics and prosecuted for his wartime activities, when he headed a paramilitary unit active both in Croatia and Bosnia.
The violence is continuing. On Wednesday, a grenade was lobbed into the offices of a prominent anti-Seselj activist, Ljubomir Rankov. Mr Rankov, another ethnic Croat, had been branded with the Ustasha label in Mr Seselj's paper the day before.
What does Mr Seselj hope to gain? According to Natasa Kandic, a human rights campaigner who is spearheading the anti-Seselj movement, it is a combination of political capital and money for the forthcoming campaign for the Serbian presidency. "He wants to attract refugees to live in Zemun and play on their feelings that they have a right to treat Croats they way that Croats have treated them," she said.
And the money? According to the newspaper Dnevni Telegraf, Mr Seselj has expropriated 1,500 hectares of land in Zemun and sold it, either for profit or on the cheap as a favour to refugees. A municipal football pitch has been flogged off, while the Zemun synagogue has been rented out for 5,000 German marks a month and converted into a disco.
Mr Seselj has also issued licences for hundreds of prefabricated street- stalls, each worth more than 3,000 marks to his office. Mr Seselj has promised to use the money to build schools and community centres, but it seems more likely it will gostraight into his election fund.
The one person able to stop Mr Seselj is Mr Milosevic, who may decide his antics are too embarrassing. Mr Milosevic has shamelessly used Mr Seselj in the past to stir up nationalist sentiment, but he has also turned against him when it suits him.
In 1994, when Mr Milosevic was refashioning himself as a man of peace, Mr Seselj was jailed for three months for beating up a fellow deputy in parliament. He was jailed again the following year for stirring up trouble in Kosovo - even though Mr Milosevic launched his own career by doing exactly the same.
Quite what purpose Mr Seselj is now serving is not clear, although it is almost certainly linked to September's presidential elections. One spin-off will be that Mr Milosevic seems almost palatable in comparison.