Transmission system, in particular for a motor vehicle, comprising, about an axis of rotation of axial orientation, at least: - a dual-clutch mechanism comprising a first clutch and a second clutch, each clutch (E1, E2) comprising a lever (44, 62), such as a diaphragm, intended to cooperate with a pressure plate (34, 54), which is coupled in rotation to a cover (18, 14), in order to clamp a friction disc (40, 56) between a reaction plate and the said pressure plate (34, 54), the said clutches (E1, E2) being respectively intended to selectively couple, to a drive shaft able to be rotated by an engine, a first shaft and a second shaft which are, on the one hand, each connected to one of the friction discs (40, 56) and, on the other hand, intended to be connected to a gearbox, and - a control device which, associated with the said mechanism, comprises actuating means which, able to respectively actuate the first lever of the first clutch and the second lever of the second clutch, are selectively controlled to allow gear ratios of different parities to be shifted, - at least the dual-clutch mechanism and the control device are pre-mounted to constitute a module forming a unitary assembly and the said module is securely mounted to a support means which, connected to the drive shaft, integrally supports the module, characterized in that the module comprises axial adjusting means intended to make it possible, prior to its assembly on the support means, to axially position the dual-clutch mechanism and the means for actuating the control device in a defined axial position corresponding to a "nominal" position, the second clutch of the mechanism comprising a second cover which is produced in at least two parts, a front part and a rear part respectively, which are able to slide axially with respect to one another so as to allow an axial adjustment until the said defined nominal position is reached. - a dual-clutch mechanism comprising a first clutch and a second clutch, each clutch (E1, E2) comprising a lever (44, 62), such as a diaphragm, intended to cooperate with a pressure plate (34, 54), which is coupled in rotation to a cover (18, 14), in order to clamp a friction disc (40, 56) between a reaction plate and the said pressure plate (34, 54), the said clutches (E1, E2) being respectively intended to selectively couple, to a drive shaft able to be rotated by an engine, a first shaft and a second shaft which are, on the one hand, each connected to one of the friction discs (40, 56) and, on the other hand, intended to be connected to a gearbox, and - a control device which, associated with the said mechanism, comprises actuating means which, able to respectively actuate the first lever of the first clutch and the second lever of the second clutch, are selectively controlled to allow gear ratios of different parities to be shifted, - at least the dual-clutch mechanism and the control device are pre-mounted to constitute a module forming a unitary assembly and the said module is securely mounted to a support means which, connected to the drive shaft, integrally supports the module, characterized in that the module comprises axial adjusting means intended to make it possible, prior to its assembly on the support means, to axially position the dual-clutch mechanism and the means for actuating the control device in a defined axial position corresponding to a "nominal" position, the second clutch of the mechanism comprising a second cover which is produced in at least two parts, a front part and a rear part respectively, which are able to slide axially with respect to one another so as to allow an axial adjustment until the said defined nominal position is reached.