While it’s not exactly like studying the order of Politburo members standing atop Lenin’s Mausoleum, Russia-watching in the era of Vladimir Putin has increasingly had to fall back on the kind of tea-leaves reading that characterized Sovietology. Today’s May Day rallies in Moscow were a case in point.

The opposition Communist Party of the Russian Federation (KPRF) held its traditional May 1 demonstration at the capital’s Revolution Square. Russia is on the eve of a crisis, Communist leader Gennady Zyuganov proclaimed to an estimated 13,500 supporters. The country, he explained, is “more and more subordinated to American capital,” its “system of administration” is becoming degraded and “mass internal dissatisfaction” is on the rise. More interesting than the KPRF rally, however, was what was happening just a short distance away, over on Red Square. A May Day demonstration was being held there for the first time in the post-Soviet period. And, in a further echo of the bad old days, the Red Square demonstration, for which 140,000 people turned out (or, perhaps more accurately, were turned out), was a de facto state-sponsored event, having been organized by the inappropriately named Federation of Independent Trade Unions (FNPR).

And while it was no big surprise that FNPR leader Mikhail Shmakov demanded the resignation of key figures in Prime Minister Mikhail Kasyanov’s cabinet–specifically those in the economic bloc headed by Economic Development and Trade Minister German Gref, which continues to push for an end to various Soviet-era subsidies–it was surprising, at least at first glance, that Shmakov’s trade unionists were joined by members of United Russia, the new pro-Putin party recently formed from the merger of various “centrist” groupings, including Unity and Fatherland-All Russia.

What is more, while United Russia marchers carried placards reading “Our president–Vladimir Putin” and portraits of the head of state–indeed, there is hardly a hair’s breadth of space between Putin and the new party–others openly denounced Putin’s cabinet. “Kasyanov and Gref, wake up, freeze,” read one United Russia placard, apparently referring to the government’s plan to allow state-controlled monopolies like UES, the national electricity grid headed by Anatoly Chubais, to raise tariffs. Indeed, with electricity rates for home consumers in Moscow having gone up 20 percent as of today, another United Russia placard read: “Chubais, don’t play with electricity, you’re already a big boy.” Other United Russia signs condemned Labor Minister Aleksandr Pochinok and wage arrears to state workers. Still others demanded both pay increases for policemen and an end to the “bespredel” (a Russian word connoting limitless power and total license) of state bureaucrats.