Pump assembly for a cooling system of a vehicle comprising: - an impeller group comprising an impeller rotatable around an impeller axis (X-X) and an impeller shaft extending along the impeller axis (X-X) integrally connected to the impeller to move it in rotation; - an electric group comprising an electric drive, comprising an electric motor, and an electric shaft rotatable by the electric drive; - a mechanical group comprising a mechanical drive and a mechanical shaft; - transmission means comprising a kinematic transmission assembly comprising: i) an impeller gear integrally connected to an impeller drive end of the impeller shaft opposite to the end whereon is mounted the impeller; ii) a first command gear operatively connected to the electric shaft and to the impeller gear; iii) a second command gear operatively connected to the mechanical shaft and to the impeller gear; iv) engagement/disengagement means comprising a first unidirectional clutch that operatively connects the electric shaft to the first command gear and comprising a second unidirectional clutch or a mechanical engagement/disengagement device or a electric engagement/disengagement device that operatively connects the mechanical shaft to the second command gear; wherein the impeller gear is commanded in rotation by means of engagement/disengagement means by the faster of the first command gear and the second command gear; wherein the pump assembly is characterized by the fact that the gears comprised in the kinematic transmission assembly are operatively connected in a direct way. - an impeller group comprising an impeller rotatable around an impeller axis (X-X) and an impeller shaft extending along the impeller axis (X-X) integrally connected to the impeller to move it in rotation; - an electric group comprising an electric drive, comprising an electric motor, and an electric shaft rotatable by the electric drive; - a mechanical group comprising a mechanical drive and a mechanical shaft; - transmission means comprising a kinematic transmission assembly comprising: i) an impeller gear integrally connected to an impeller drive end of the impeller shaft opposite to the end whereon is mounted the impeller; ii) a first command gear operatively connected to the electric shaft and to the impeller gear; iii) a second command gear operatively connected to the mechanical shaft and to the impeller gear; iv) engagement/disengagement means comprising a first unidirectional clutch that operatively connects the electric shaft to the first command gear and comprising a second unidirectional clutch or a mechanical engagement/disengagement device or a electric engagement/disengagement device that operatively connects the mechanical shaft to the second command gear; wherein the impeller gear is commanded in rotation by means of engagement/disengagement means by the faster of the first command gear and the second command gear; wherein the pump assembly is characterized by the fact that the gears comprised in the kinematic transmission assembly are operatively connected in a direct way. i) an impeller gear integrally connected to an impeller drive end of the impeller shaft opposite to the end whereon is mounted the impeller; ii) a first command gear operatively connected to the electric shaft and to the impeller gear; iii) a second command gear operatively connected to the mechanical shaft and to the impeller gear; iv) engagement/disengagement means comprising a first unidirectional clutch that operatively connects the electric shaft to the first command gear and comprising a second unidirectional clutch or a mechanical engagement/disengagement device or a electric engagement/disengagement device that operatively connects the mechanical shaft to the second command gear; wherein the impeller gear is commanded in rotation by means of engagement/disengagement means by the faster of the first command gear and the second command gear; wherein the pump assembly is characterized by the fact that the gears comprised in the kinematic transmission assembly are operatively connected in a direct way.