The apparatus for attachment to a non-inflatable part of a tandem, two-wheel cycle for rigidly mounting the cycle for transit purposes includes a bracket-like member adapted to be secured to the frame or other non-inflatable part of the cycle. A multi-part assembly is connected to the bracket for supporting the same for movement in longitudinal, transverse and vertical directions. The multi-part assembly includes a component adapted to be secures to the bed of a trailer or other transit vehicle. The multi-part assembly includes adjustable securing means for fixing the position of the bracket-like member.