Transmission, comprising a first circulating element (2,3) rotatable about a first rotation axis, a second circulating element (2,3) rotatable about a second rotation axis, an elongate flexible continuous transmission element which is passed around both the first circulating element (2,3) and around the second circulating element (2,3), at least one of the first and second circulating elements (2,3) comprising: - a number of contact elements which are distributed around the rotation axis of the respective circulating element for contact with the transmission element, which contact elements determine a running radius on which the transmission element is passed around the respective circulating element, - a radial guide for each of the contact elements, along which the respective contact elements can be moved to and fro radially between an inner radial position and an outer radial position, - displacement means for moving the contact elements to and fro in the radial direction between the inner and the outer position, wherein the transmission element is provided with a number of engagement elements which are provided at a regular pitch on a side facing the contact elements, and each of the contact elements comprising - a base part which is in operative contact with the radial guide and with the displacement means, and - an engagement member (152,252) which is connected to the base part and can be moved in a radial direction with respect to the base part, wherein the engagement member (152,252) of at least one of the number of contact elements of the respective circulating element is in positive-locking contact with at least one engagement element of a number of engagement elements of the transmission element, characterized in that the engagement member is also movable in the direction of rotation of the transmission element around the respective circulating element with respect to the base part of the contact element wherein the contact element furthermore comprises a connecting piece, wherein the engagement member is held to the connecting piece so as to be movable in a radial direction, wherein the connecting piece is connected to the base part so as to be movable in the direction of rotation of the transmission element around the respective circulating element with respect to the base part of the contact element wherein each contact element of the number of contact elements comprises a further spring member which is active between the base part and the connecting piece in order to move the connecting piece to a predetermined neutral position, at least when there is no contact between the engagement member and transmission element. - a number of contact elements which are distributed around the rotation axis of the respective circulating element for contact with the transmission element, which contact elements determine a running radius on which the transmission element is passed around the respective circulating element, - a radial guide for each of the contact elements, along which the respective contact elements can be moved to and fro radially between an inner radial position and an outer radial position, - displacement means for moving the contact elements to and fro in the radial direction between the inner and the outer position, wherein the transmission element is provided with a number of engagement elements which are provided at a regular pitch on a side facing the contact elements, and each of the contact elements comprising - a base part which is in operative contact with the radial guide and with the displacement means, and - an engagement member (152,252) which is connected to the base part and can be moved in a radial direction with respect to the base part, wherein the engagement member (152,252) of at least one of the number of contact elements of the respective circulating element is in positive-locking contact with at least one engagement element of a number of engagement elements of the transmission element, characterized in that the engagement member is also movable in the direction of rotation of the transmission element around the respective circulating element with respect to the base part of the contact element wherein the contact element furthermore comprises a connecting piece, wherein the engagement member is held to the connecting piece so as to be movable in a radial direction, wherein the connecting piece is connected to the base part so as to be movable in the direction of rotation of the transmission element around the respective circulating element with respect to the base part of the contact element wherein each contact element of the number of contact elements comprises a further spring member which is active between the base part and the connecting piece in order to move the connecting piece to a predetermined neutral position, at least when there is no contact between the engagement member and transmission element. - a base part which is in operative contact with the radial guide and with the displacement means, and - an engagement member (152,252) which is connected to the base part and can be moved in a radial direction with respect to the base part, wherein the engagement member (152,252) of at least one of the number of contact elements of the respective circulating element is in positive-locking contact with at least one engagement element of a number of engagement elements of the transmission element, characterized in that the engagement member is also movable in the direction of rotation of the transmission element around the respective circulating element with respect to the base part of the contact element