The summit of G8 leaders at Gleneagles will be policed by the biggest ever UK mobilisation of officers.
Saturday's protest was described by police as 'trouble-free'
Some 10,600 officers from all over the UK will police the summit and related-events around Edinburgh.
Lothian and Borders Police say they are ready to deal with a planned anarchist protest in Edinburgh on Monday.
Meanwhile, almost 100 road sweepers have helped to clean up the city after Saturday's march of an estimated 225,000 anti-poverty protesters.
They made their protest as part of the Make Poverty History campaign as musicians performed in Live 8 concerts around the globe.
The marchers called for the G8 leaders at the summit to make a commitment to tackle poverty in Africa.
People from all walks of life rubbed shoulders with celebrities including actor Pete Postlethwaite, comedian Eddie Izzard and singer Daniel Bedingfield.
The march coincided with the Live 8 concerts in 10 cities around the world, including London.
Lothian and Borders Police paid tribute to the crowd for the trouble-free atmosphere and organisers for their "meticulous planning and co-operation".
But a spokesman said they were concerned about the Carnival for Full Enjoyment, due to be held on Monday, because of the prospect of anarchists disrupting the centre of Edinburgh.
The event has the backing of anti-capitalist groups the Wombles and Dissent.
Up to 10,000 people are expected to blockade the Faslane naval base in Clyde in a further anti-G8 event.
On Sunday, Moulin Rouge and Trainspotting star Ewan McGregor launched a three-day children's "C8 summit", organised by Unicef, in Dunblane.
Young delegates from all over the world will draw up a manifesto about issues they think the G8 should address.
Other events staged in Edinburgh on Sunday included a Stop the War Coalition protest and the G8 Alternative Summit where more than 200 international speakers were given a platform.
About 2,000 police officers from England and Wales made their way to Scotland on Sunday with another 4,000 expected before Wednesday.
Officers drafted in from other parts of Scotland take the total number of officers policing the summit, which begins on Wednesday, to 10,600.
Meanwhile, US President George W Bush has ruled out his country's backing for any Kyoto-style deal on climate change at the G8 summit.
He told ITV he was keen to look at new technologies as a way of tackling global warming.
Prime Minister Tony Blair will be looking for deals on climate change and Africa when he hosts the summit.