The Black Sea town of Poti has been a port for 2,500 years. It has been home to the Greeks and the Romans. But now this hot, dusty, urban centre has another claim to fame - as the latest frontline in the new cold war.

Out on the Black Sea, 10 Nato battleships led by the USS McFaul have been steaming towards Poti, apparently on a mission to deliver humanitarian aid. On land, the Russians have dug in just outside town - parking their armoured personnel carriers on a grassy verge next to the main road.

The crisis began earlier this month when Russia bombed the port during its invasion of Georgia, killing five people and sinking Georgia's tiny naval fleet.

During my recent visit, the damage caused by Russian soldiers wasn't hard to spot. They had ransacked store rooms and trashed Poti's coastguard building, upturning filing cabinets and stomping on a portrait of Georgia's leader, Mikheil Saakashvili.

On Friday, much of Russia's army withdrew from Georgia. But in Poti, they stayed - establishing a checkpoint 7km outside town. The Georgians - 1,000 of whom staged a noisy protest at the weekend - accuse them of looting; Russian soldiers have been seen driving off with photocopiers. US warships, meanwhile, have been docking at the seaside resort Batumi, just down the coast.

Russia's president, Dmitry Medvedev, says they are smuggling arms to the Georgians, and the Russians have shown off five US Humvees left behind by the Americans following a recent US-Georgian military exercise.

The coast is popular with Georgia's elite; villas with swimming pools nestle among tall fir trees. There is no sign here of an geopolitical standoff between Moscow and the west. The EU says Russia's presence in Poti is in breach of a ceasefire agreement signed by Medvedev; Russia says it isn't, and doesn't appear to care.

At every stage of this crisis, Russia's prime minister, Vladimir Putin, has assumed it will be the west that blinks first. So far he has been proved right. Expect the Russians - like the Greeks before them - to stay in Poti for a while yet.