Chronograph mechanism for a timepiece comprising a clockwork movement, this chronograph mechanism comprising: - a first sweep-hand mobile provided for carrying a first sweep hand for indicating a measured time, - a first brake capable of angularly immobilising the first sweep-hand mobile, - a second sweep-hand mobile which is provided for carrying a second sweep hand for indicating a measured time and which rotates on the same axis of rotation (x-x') as the first sweep-hand mobile, - a second brake capable of angularly immobilising the second sweep-hand mobile, - an intermediate chronograph mobile which rotates on the same axis of rotation (x-x') as the first and second sweep-hand mobiles (30, 35) and is arranged to transmit a drive from the clockwork movement to the first and second sweep-hand mobiles (30, 35), - a first return device capable of returning the first sweep-hand mobile to a predetermined angular position relative to the intermediate chronograph mobile in the absence of angular immobilisation of this first sweep-hand mobile by the first brake, - a second return device capable of returning the second sweep-hand mobile to a predetermined angular position relative to the intermediate chronograph mobile in the absence of angular immobilisation of this second sweep-hand mobile by the second brake, characterised in that it comprises a control system (P1, P2, P3, 60, 701-714) comprising a coordination device which is arranged to maintain the first and second brakes (50a, 50b) in two alternative configurations, namely - a first configuration in which the first brake is in an inactive state, thereby allowing the first sweep-hand mobile to rotate freely, and in which the second brake is in an active state, thereby angularly immobilising the second sweep-hand mobile, and - a second configuration in which the second brake is in an inactive state, thereby allowing the second sweep-hand mobile to rotate freely, and in which the first brake is in an active state, thereby angularly immobilising the first sweep-hand mobile. - a first sweep-hand mobile provided for carrying a first sweep hand for indicating a measured time, - a first brake capable of angularly immobilising the first sweep-hand mobile, - a second sweep-hand mobile which is provided for carrying a second sweep hand for indicating a measured time and which rotates on the same axis of rotation (x-x') as the first sweep-hand mobile, - a second brake capable of angularly immobilising the second sweep-hand mobile, - an intermediate chronograph mobile which rotates on the same axis of rotation (x-x') as the first and second sweep-hand mobiles (30, 35) and is arranged to transmit a drive from the clockwork movement to the first and second sweep-hand mobiles (30, 35), - a first return device capable of returning the first sweep-hand mobile to a predetermined angular position relative to the intermediate chronograph mobile in the absence of angular immobilisation of this first sweep-hand mobile by the first brake, - a second return device capable of returning the second sweep-hand mobile to a predetermined angular position relative to the intermediate chronograph mobile in the absence of angular immobilisation of this second sweep-hand mobile by the second brake, - a first configuration in which the first brake is in an inactive state, thereby allowing the first sweep-hand mobile to rotate freely, and in which the second brake is in an active state, thereby angularly immobilising the second sweep-hand mobile, and - a second configuration in which the second brake is in an inactive state, thereby allowing the second sweep-hand mobile to rotate freely, and in which the first brake is in an active state, thereby angularly immobilising the first sweep-hand mobile.