Children as young as two years old have been caught engaged in criminal activities in the past year.
Two children were reported for vandalism in Dumfries and Galloway
Figures across Scotland have shown dozens of youngsters under the age of eight have been stopped by police between March 2006 and April 2007.
In Strathclyde, a total of 48 children were found committing offences - including one aged just two.
Ten such incidents were dealt with in Dumfries and Galloway - including two four-year-olds engaged in vandalism.
Ch Supt John Pollock of Strathclyde Police said problems with children aged seven and under were few and far between.
He said that although a crime report was generated, no crime could be committed by someone under eight because they are considered to be too young to tell right from wrong.
"Moreover, in relation to total detected crime, the total attributable to children under eight years of age equates to only 0.036% of all crimes and offences detected," he said.
"The vast majority of crime is, of course, committed by adults."
Insp Chris Hope, from Dumfries and Galloway Police, confirmed it had dealt with 10 children under eight in the past year.
However, he said the trend for such incidents was declining.
"The figures mirror the previous year, which showed a 33% reduction from 2004/05 figures," he said.
"It is disappointing that anyone commits any offence but can be more worrying when it is someone so young.
"The force policy for all young offenders is to ensure that the appropriate support is available to them and their families."
A Scottish Government spokesperson said it was determined to stop young people getting involved in crime.
"Tackling a problem like this means getting at the root causes of crimes - especially drink, drugs and deprivation," he said.
"We want to give young people more opportunities, a bit of self-esteem, and for them to learn to take responsibility for their actions.
"Clearly that also requires parents to acknowledge their responsibilities to teach young people right from wrong."
He said the government was committed to achieving this by funding a range of projects promoting positive parenting.