A continuously variable transmission comprising: - a housing, - an input shaft bearing supported in the housing, - an output shaft bearing supported in the housing, - a pulley with two pulley wheels (7A, 7B) spaced apart from each other and provided with contact surfaces running obliquely relative to a central axis, which is an axis of rotation of the pulley, and facing each other, of which pulley wheels at least one pulley wheel can be displaced in axial direction relative to the other pulley wheel, - a transmission element located between the two pulley wheels and provided with two lateral surfaces facing each other which are in contact with the contact surfaces of the pulley wheels, - an adjusting mechanism for varying the travel radius of the transmission element, characterized in that - the pulley can be turned in the direction of rotation while the transmission ratio is being adjusted, but is fixed relative to the housing in the direction of rotation during the transmission of power, - the transmission element is formed by a partly annular carrier carrying a plurality of contact elements, which contact elements are provided with said two lateral surfaces, and the transmission element rotates on rotation of the input shaft due to the contact between the contact surfaces of the pulley and the lateral surfaces of the contact elements, - the continuously variable transmission furthermore includes a shaft journal connected to the input shaft on which journal the transmission element is bearing supported, - the continuously variable transmission further includes a constant velocity joint of which a first joint portion is connected to the transmission element and of which a second joint portion is connected to the output shaft. - a housing, - an input shaft bearing supported in the housing, - an output shaft bearing supported in the housing, - a pulley with two pulley wheels (7A, 7B) spaced apart from each other and provided with contact surfaces running obliquely relative to a central axis, which is an axis of rotation of the pulley, and facing each other, of which pulley wheels at least one pulley wheel can be displaced in axial direction relative to the other pulley wheel, - a transmission element located between the two pulley wheels and provided with two lateral surfaces facing each other which are in contact with the contact surfaces of the pulley wheels, - an adjusting mechanism for varying the travel radius of the transmission element, characterized in that - the pulley can be turned in the direction of rotation while the transmission ratio is being adjusted, but is fixed relative to the housing in the direction of rotation during the transmission of power, - the transmission element is formed by a partly annular carrier carrying a plurality of contact elements, which contact elements are provided with said two lateral surfaces, and the transmission element rotates on rotation of the input shaft due to the contact between the contact surfaces of the pulley and the lateral surfaces of the contact elements, - the continuously variable transmission furthermore includes a shaft journal connected to the input shaft on which journal the transmission element is bearing supported, - the continuously variable transmission further includes a constant velocity joint of which a first joint portion is connected to the transmission element and of which a second joint portion is connected to the output shaft.