A parking brake arrangement for a brake unit—also having a service brake actuator—has in a housing (4) a clock spring (10) for exercising a rotary motion at will on a parking brake gear wheel (8) in drive connection with a device (5-7) for delivering brake force from the brake unit (1). The arrangement has two axially movable control sleeves (15, 16) in drive connection with the clock spring (10). The control sleeves form clutches (8′, 15 and 12, 16, respectively) with the parking brake gear wheel (8) and the housing (4), respectively. There are means (13, 18-21) for controlling the axial movements of the two control sleeves and the engagement of the two clutches in such a way that either one of them is always in engagement.