Timepiece including: - a timepiece mechanism (6, 8, 10) capable of switching between a specific first state and a specific second state; - a switching device (4; 4A; 4B; 4C) arranged to be able to switch the timepiece mechanism between said first and second states, said switching device including a control member (16; 16C), which extends in a general plane in which it is subjectable to a movement under the action of an actuation device (22, 24) of said control member, and a switching member (12; 12A; 12B; 12C) at least one part of which is arranged to be subjectable to a movement having a component orthogonal to said general plane; the switching device being arranged such that said at least one part of the switching member is capable of passing on demand from a first stable axial position to a second stable axial position, to cause a first switch of the timepiece mechanism between the first state and second state thereof, and from the second stable axial position to the first stable axial position to cause a second switch of the timepiece mechanism between the second state and the first state thereof; characterized in that the control member is arranged to pivot about an axis of rotation which is perpendicular to said general plane, so as to be drivable step-by-step in a given direction of rotation, successively into a plurality of distinct angular positions; in that the control member and the switching member respectively include a first magnetic structure and a second magnetic structure arranged to exhibit a magnet interaction therebetween; in that one of the first and second magnetic structures includes at least a first magnetic pole and the other of said two magnetic structures includes at least a second magnetic pole and a third magnetic pole with opposite polarities, the first and second magnetic structures being arranged such that, in a first angular position of the control member of said plurality of distinct angular positions, the first magnetic pole mainly exhibits a first magnetic interaction with one of the second and third magnetic poles, and such that, in a second angular position of this control member of the plurality of distinct angular positions, this first magnetic pole mainly exhibits a second magnetic interaction with the other of the second and third magnetic poles, the first and second magnetic interactions producing on the switching member a first magnetic force and a second magnetic force respectively, both mainly oriented along said axis of rotation in opposite directions, allowing said at least one part of said switching member to be moved from the first stable axial position to the second stable axial position and vice versa; and in that said at least one part of the switching member is subjected to an alternate movement between the first and second stable axial positions thereof when the second magnetic structure is driven in rotation step-by-step in said given direction of rotation. - a timepiece mechanism (6, 8, 10) capable of switching between a specific first state and a specific second state; - a switching device (4; 4A; 4B; 4C) arranged to be able to switch the timepiece mechanism between said first and second states, said switching device including a control member (16; 16C), which extends in a general plane in which it is subjectable to a movement under the action of an actuation device (22, 24) of said control member, and a switching member (12; 12A; 12B; 12C) at least one part of which is arranged to be subjectable to a movement having a component orthogonal to said general plane;