It seemed logical to expect that the two government employees would disapprove of such lack of respect. But in Belgrade the spirit of rebellion is infectious. With scant loyalty to their boss, the two men gave a thumbs up to the demonstrators, whose main demand has been the recognition of opposition election victories in November, and whose main desire is the fall of Mr Milosevic himself.
Even policemen seem eager to change sides. One of the few on duty yesterday suggested his heart was with the demonstrators: "I would be glad to tell you what I think - but I don't dare."
In a sense, it was the party to end all parties. No sign of drugs, and little alcohol. Just a celebration, where hundreds of thousands seemed intoxicated by the possibility of change. As one headline put it: "Happy New Serbia." Or, in the words of the liberal daily Nasa Borba: "The energy which astonished the world."
Long before midnight on Monday night, it was well nigh impossible to move near Republic Square, venue for the celebration. Some of Serbia's best-known actors and musicians were due to appear, to see in the new year according to the Orthodox Church calendar.
The streets were thronged with an estimated half million Serbs, who together created a deafening cacophony of little plastic whistles, signifying "game over!" for Mr Milosevic. But despite the exploding firecrackers the gathering passed off peacefully. In the official media, the event was passed over in near silence. But the reality could not be ignored: this is the beginning of something different for Serbia.
This was a brighter, more cheerful Belgrade than has been seen in recent years. The jubilation did not come from victory. Yesterday's key retreat, when the opposition's election victories in the cities of Belgrade and Nis were acknowledged, came hours after the partying protesters had gone to bed. It came from self-confidence: the belief in Belgrade that though muddy snow lies round about,the political ice age is over.
Jelena Vencl, 22, a student, said: "Now we've got a new spirit. I think about my future. I can be a scientist anywhere in the world. But I think Serbian society is changing, and I want to stay here." Nikola Urosevic, 38, an electrical engineer, insisted: "It has to be a happy new year. Any change will be for the better. This fool has to go."
"Forces of chaos and madness", says a favourite demonstrators' badge, mocking official accusations. In reality, the chaos and madness seem to emanate from the government. Gordana Markovic, a dentist in her fifties, said: "If you had asked me two months ago, I would have said it's impossible [for so many people to come together in opposition to the government]. But now there's no fear."
After fireworks at midnight, the crowds streamed away from Republic Square along the Street of Serbian Rulers (Marshal Tito Street, as it used to be), blowing whistles and trumpets and enjoying the right to walk the streets: the ban on demonstrations had been suspended, for what was allegedly just a new year celebration.
Then they streamed back into the square, listening to bands playing against a back-drop which proclaimed "Studentski Protest 96-97." The atmosphere in Republic Square in the early hours of yesterday was astonishingly similar to the mood in Prague in November 1989, before and during the fall of the Communist regime.
But one difference may be crucial. In Prague, students who spearheaded the protest shared an outlook with the opposition, most notably Vaclav Havel. Here, by contrast, few of the students have much time for the organised opposition. On Monday night, Vuk Draskovic, one of the opposition leaders with a nationalist past, attacked students as "idiots". They were failing to acknowledge the role of Mr Draskovic.
Whatever happens, Belgrade will not be the same again. That is a step forward. Branko, a 45-year-old builder, said: "It's not Milosevic's town anymore. And he knows that."