Abstract: Gear selection and engagement device for a motor vehicle transmission, the said device comprising a shaft moving in the direction of and round its own axis and constituting a support for a number of hubs each integral with a corresponding fork; the said device also comprising a first set of teeth projecting radially from the said shaft and being axially and torsionally integral with the same, one of the said hubs being arranged between two adjacent teeth on the said first set; the said device also comprising a second set of teeth projecting radially from the said shaft, being torsionally integral with it and being axially fixed in relation to the transmission case; each of the said hubs having at least one pair of axial grooves designed to accommodate the teeth in the said first and second set; the said grooves being arranged round the circumference of each hub in such a preset manner that, for a preset angular position of the said shaft corresponding to a preset gear selection, all the teeth in the first set