An improved, simple rack for the secure transport of bicycles and small motorcycles in the bed of a pickup truck or trailer without clamping, strapping or disassembly of the cycle, and with minimal obstruction of the load-carrying bed floor, has individual cycle wheel receptacles with both fixed and spring-loaded wheel clamping brackets, that are secured to at least one rack rail assembly that is secured to opposite sides of the truck or trailer bed. In order to secure a cycle in the rack, a front or rear wheel of the cycle is lifted up and pushed into the wheel receptacle between the fixed and spring-loaded wheel clamping brackets. In order to unload the cycle, the wheel is pushed against the spring-loaded wheel clamping bracket, thereby releasing the wheel from the fixed wheel clamping bracket, and is, then, pulled upwardly from the wheel receptacle.