The 13 and 14-year-old boys were involved in a car chase in which they tried to ram a pursuing police car, a spokeswoman said as police complained that the case showed the lack of secure units for young offenders.
The boys, who had been arrested 39 times in the past year, were arrested again after a 71- year-old woman's handbag was snatched in Newcastle upon Tyne.
They were handed over to council care at 1.50am yesterday but just over two hours later were on the run again, this time in a stolen Metro City car.
They eventually abandoned the car and were re-arrested as they tried to flee and taken to Newcastle's Newburn police station.
Superintendent David Swift, the city's West End sub-divisional commander, said: 'While police officers are making arrests, there are cases where some young offenders are constantly arrested but continue to re-offend.'
This was due to the lack of secure units suitable for holding such boys. 'It is a frustrating situation for officers to be in, especially when a re-arrest does not deter,' he said.