Nowhere is their presence more ominously felt in eastern Ukraine than in the small, once-insignificant industrial town of Sloviansk.
For some weeks now these mysterious masked gunmen dressed in green military fatigues have patrolled the streets of this drab, run-down community of gloomy concrete buildings.
Few people worldwide had heard of Sloviansk until the pro-Russian separatist unrest that now grips the east of Ukraine. Today, though, Sloviansk sits at the heart of a geopolitical struggle that has pitched the West and Moscow into a crisis not seen since the Cold War.
Described by Ukraine's interior ministry as "the most dangerous place in Ukraine", speculation has focused on what officials also describe as "the presence in the town of foreign saboteurs and illegal armed groups".
Put another way, Kiev and others are firmly of the belief that Russia has already embarked on an invasion by stealth that has left the green men well embedded within Sloviansk and elsewhere across eastern Ukraine.
Just off Sloviansk's Karl Marx Street, where a cluster of armoured personnel carriers sit behind heavily sandbagged emplacements, the gunmen seemed particularly jumpy yesterday.
"No, no," ordered one wearing the ubiquitous ski mask and carrying an assault rifle, who leaned forward and twisted the neck strap on my camera ensuring that the lens faced inwards towards my chest.
Never keen to be photographed, there has been a heightened sensitivity among the ranks of the green men over the last few days after the US State Department released images it claimed proves armed separatists in eastern Ukraine are actually Russian military or intelligence officers.
The pictures, first handed over by Ukraine's state security service to the Organisation for Security and Co-operation in Europe (OSCE) before being distributed by the Americans, are said to be evidence that Russian special forces are operating on the ground in contested towns like Sloviansk. Their release coincides too with a visit to the Ukrainian capital, Kiev, by US Vice-President Joe Biden.
Yesterday, Mr Biden reiterated Washington's support for the new pro-Western government there.
The US stands with Ukraine's new leaders against "humiliating threats" insisted the US Vice-President in an apparent reference to Russia.
Back on the ground in Sloviansk yesterday, feelings were running high too as the bodies of three pro-Russian activists shot dead at a checkpoint on Easter Sunday lay in open coffins ready for burial.
In a church near the centre of the town an orthodox priest recited prayers for the dead as outside a crowd of people chanted "Glory to the Heroes of the Donbass", the local name for this Don River region.
Over the last few days beneath a giant statue of Lenin in Sloviansk's main square, people have come to pay their respects to the three dead men whose faces look out from posters pasted on a plinth.
Nearby stands the town hall, its entrance heavily sandbagged and guarded by the ever-present green men.
"Look, they can't even hang the Donbass flag the right way up," commented one young local man, pointing to the red, blue and black horizontal-striped flag that was hanging the wrong way round over a wall of sandbags.
Barely had he spoken than the flag was taken down before being hoisted right way up this time.
"It will only be better here when these people leave," insisted 17-year-old Valentin, a local student, speaking of the "outsiders" he says have come to Sloviansk of late.
Asked if he meant Russians, his reply was unequivocal.
"This is a fairly small community, we notice when outsiders come, especially those carrying guns, of course they are Russians."
Time and again while travelling around the city there are glimpses of the green men positioned in strategic places. Their weapons, equipment, body armour and radio handsets are often state of the art, in keeping, say some military analysts, with those of Russian special forces troops.
Other masked and armed men around Sloviansk's streets are of course local Ukrainians. But even they, with their well-disciplined and organised deployment, are a far cry from the teenage local thugs wielding baseball bats and iron bars who comprise the pro-Russian separatist foot soldiers in other areas of eastern Ukraine.
While these teenagers are still to be found among members of the self-described 'Donetsk Self-Defence Force' that guards the roads leading into Sloviansk, they are clearly under orders from men whose distinctive military bearing marks them out as soldiers or having had some kind of military training.
Yesterday, as military and intelligence analysts continued to debate the significance of the photographs made public by the US State Department, locals in Sloviansk had their own take.
"Let me put it this way," said one Sloviansk resident wryly, to much laughter from others around him in the town square.
"Green men, red men, you can call them what you want, but they are not from Mars, but Moscow."