Two teenagers have been arrested after messages were posted on Facebook allegedly inciting others to commit acts of disorder.
A 16-year-old was detained during an operation in Glasgow's south side at 12:40 on Monday.
He has been charged with breach of the peace and is due to appear at Glasgow Sheriff Court on Wednesday.
An 18-year-old man is expected to appear at Dundee Sheriff Court over similar allegations.
Tayside Police said they were following other positive lines of inquiry to identify others who may be inciting others to cause public disorder.
The arrests come after rioting and looting in London at the weekend spread to other English cities.
Police said they were monitoring social networking sites closely and would take "decisive action" to prevent violence.
The Strathclyde force said there was no intelligence "at this time" to suggest that there was any trouble planned.
Earlier, the Association of Chief Police Officers in Scotland confirmed that forces here were on standby to help colleagues in England if requested.
There have been three nights of violence in London since a 29-year-old man was shot dead in Tottenham by police on Thursday.
A peaceful protest over the death of Mark Duggan was followed by violence which spread to other parts of the city on Sunday.
A third night of unrest saw violence spread outside London to Birmingham, Manchester, Liverpool, Nottingham and Bristol.