The maintenance device comprises a robot (2) for carrying out maintenance work in a remote-controlled or programmed way in the maintenance region. The robot (2) comprises a supporting part (2a) connected to a clamping support (3) secured to a means (4) of transporting the maintenance device (1) between an introductory region and the maintenance region. The clamping support (3) comprises clamping shoes (11, 13a, 13b) which can be moved in roughly parallel and opposite directions so as to clamp the maintenance device (1) in the maintenance region. The transport means (4) may be constructed in the form of a carriage comprising two motorized wheelsets. The device and the method of the invention make it possible in particular to carry out machining or inspection work inside primary pipes of a pressurized water nuclear reactor.