Vehicle seat with a headrest

The motor vehicle's seat has a headrest (1) which is vertically adjustable by a first support rod (2,3) in a mounting provided in a support structure (6) fixed on the seat back. The mounting encompasses the support rod with a radial clearance, and a clamping element is movable by a remotely controlled drive between a fixed position and released position. The clamping element in the fixed position applies a clamping force to the support rod transversely to its longitudinal direction, whereby the mounting rod by a section of its circumferential surface is pressed against the mounting.