System for moulding and fitting a first part and a second part, the moulding and fitting system comprising: - at least two parallel guide rails; - for each guide rail, a carriage which is fitted such as to be mobile in translation on the guide rail, between a downstream stop and an upstream stop; - at least one first series of moulds, each first mould being designed to mould one of the first parts, each first series of moulds being supported by an assembly bar; - for the or each assembly bar and for each carriage, a manoeuvring gear which is fitted on said carriage and is mobile in rotation around an axis of rotation perpendicular to the direction of displacement of the carriages, said assembly bar being fitted on each of the manoeuvring gears; - for the or each first series of moulds, a second series of moulds, each second mould being designed to mould one of the second parts; - each assembly bar being mobile in rotation between a first position, in which each first series of moulds is not opposite the corresponding second series of moulds, and a second position in which each first series of moulds is opposite the corresponding second series of moulds, and each second series of moulds being fitted such as to be mobile between a low position, in which the first part and the second part are not fitted together, and a high position in which the first part and the second part are fitted together; - for each carriage, a rack which is designed to be displaced parallel to said guide rail, and to engage the manoeuvring gear(s) of said carriage; - for each carriage, a locking device which is designed to lock said carriage alternatively with the rack and the guide rail; - for each rack, an activation device which is designed to displace said rack. - at least two parallel guide rails; - for each guide rail, a carriage which is fitted such as to be mobile in translation on the guide rail, between a downstream stop and an upstream stop; - at least one first series of moulds, each first mould being designed to mould one of the first parts, each first series of moulds being supported by an assembly bar; - for the or each assembly bar and for each carriage, a manoeuvring gear which is fitted on said carriage and is mobile in rotation around an axis of rotation perpendicular to the direction of displacement of the carriages, said assembly bar being fitted on each of the manoeuvring gears; - for the or each first series of moulds, a second series of moulds, each second mould being designed to mould one of the second parts; - each assembly bar being mobile in rotation between a first position, in which each first series of moulds is not opposite the corresponding second series of moulds, and a second position in which each first series of moulds is opposite the corresponding second series of moulds, and each second series of moulds being fitted such as to be mobile between a low position, in which the first part and the second part are not fitted together, and a high position in which the first part and the second part are fitted together; - for each carriage, a rack which is designed to be displaced parallel to said guide rail, and to engage the manoeuvring gear(s) of said carriage; - for each carriage, a locking device which is designed to lock said carriage alternatively with the rack and the guide rail; - for each rack, an activation device which is designed to displace said rack.