The boys, aged 12, 15, 16 and 17, were arrested on Tuesday 27 October following a report that a stolen motorbike had been seen being ridden dangerously in the Alfreton area.
Officers attended and spotted a number of people on four motorbikes in Long Meadow Road, who then sped off.
Two of the bikes were seen again by officers in Rodgers Lane, and a pursuit followed.
With support from the National Police Air Service helicopter, officers caught up with the two bikes in The Chine, South Normanton, where the boys were arrested.
The 12-year-old boy was additionally arrested on suspicion of possessing CS gas, and the 16-year-old on suspicion of possessing a bladed article.
A third bike was later found abandoned in Rodgers Lane.
Derbyshire Constabulary is urging anyone with concerns about anti-social bike use or potentially stolen vehicles to report them using the following methods:
Information can also be provided anonymously to the independent charity Crimestoppers by calling 0800 555 111 or visiting the Crimestoppers website.