A conveying system for material samples, especially medical samples, comprising a conveyor track forming at least one conveying section and at least one self-propelled sample holder displaceable along the conveying section holding a sample vessel. The holder comprises a drive motor, an energy accumulator for supplying the motor with energy and a friction wheel, drivable by the motor, for transmitting force onto the track. The track has at least one guide structure forming the conveying section. The holder has exactly one wheel on a lower side facing the track in operation, and has at least two sliding elements which rest on the track in operation and slide along the track's surface, the sliding elements and the wheel lying on the vertices of a triangle. The holder, on its lower side, has a guide element for cooperation with the guide structure in the track to guide the holder along the conveying section.