An atrio-ventricular transcatheter valve prosthesis (1) for the functional replacement of an atrio-ventricular valve (9) in a connection channel (18), which has a circumferential connection channel wall structure (18 '), between an atrial chamber (3) and a ventricular chamber (5) of a heart (7), comprising - an internal device (19) configured to be arranged inside an connecting channel (18), in which the internal device ( 19) has a circumferential support structure (21) that is radially expandable, and that has a valve (22) attached to the circumferential support structure (21), in which the circumferential support structure (21) of the internal device (19) ) is tubular in shape and extends along an axis and has two axial ends (21 ', 21 "), in which the internal device (19) will be arranged with its circumferential support structure (21) within the ring of the native valve or in an indoor position cer from the same and between the leaflets of the native valve (11), and - an external device (25) configured to be disposed outside the connection channel (18), in which the external device is configured to extend at least partially around the internal device (19) at a radial distance to the internal device (19), and in which the internal and external devices (19, 25) are configured to form a clamping mechanism to hold the wall structure of the circumferential connection channel (18 ') between them, in which the external device (25) will be arranged around the outside of the leaflets of the native valve (11) near the valve ring, in which the leaflets of the native valve (11) are part of the wall structure of the connection channel (18 ') in which the external device (25) is configured to form a ring (26), so that it extends circumferentially around the wall structure of the connection channel cir cunferential (18 '), between, and at a distance from the axial ends of the internal device (19), in which the circumferential support structure (21) of the internal device (19) c
