BALAKLAVA, Ukraine — Oleg and Irina Shevtsov, a proudly patriotic Russian couple, took their three young children on an outing Sunday morning to admire a long column of Russian troops and armor that, a day earlier, had secured their Crimean town’s dusty main street. By the time the family got there, however, the Russians had all vanished, disappearing as quickly and mysteriously as they had appeared.

“The children were very disappointed,” said Mr. Shevtsov, a computer expert who, like many others in this nominally Ukrainian but zealously pro-Russian region, was delighted when he first learned of what the Ukrainian government in Kiev and much of the world has condemned as an illegal military occupation.

A day after what seemed to be the start of a full-scale Russian offensive, however, Mr. Shevtsov and just about everyone else are trying to figure out what it is exactly that President Vladimir V. Putin of Russia is up to. The swirling drama in Crimea has produced not so much a phony war — as the early and almost entirely peaceful phase of World War II was known — but a strange phantom war in which heavily armed men come and go, mostly in masks and in uniforms shorn of all markings, to confront an enemy nobody has actually seen, except in imaginations agitated by Russian television.

At the headquarters of a newly established pro-Russian self-defense force in the city of Sevastopol on Sunday, would-be recruits gathered beneath a Russian flag and frothed with fury at the “fascists” who they believe have seized power in Kiev and are now preparing to flood into Crimea to plunder and kill anybody who speaks Russian instead of Ukrainian.