A transport system, in particular an airport baggage handling system, includes a container having an underside formed with a grooved recess which defines a leading edge and a trailing edge, as viewed in a transport direction of the container. The transport system has at least one incline conveyor which is constructed to define a convexly curved transport path for transporting the container through engagement of the grooved recess, whereby the incline conveyor supports only the leading and trailing edges of the recess of the container, as the container is moved in the transport direction. This ensures a stable travel of the container along the convexly curved transport path.