A transcatheter atrio-ventricular valve prosthesis for functional replacement of an atrio-ventricular valve in a connection channel, having a circumferential connection channel wall structure, between an atrial chamber and a ventricular chamber of a heart, comprising - an inner device configured to be disposed in an interior of the connection channel, the inner device having a circumferential support structure which is radially expandable, and having a valve attached to the circumferential support structure, wherein the circumferential support structure of the inner device is of tubular shape and extends along an axis and has two axial ends (21', 21"), wherein the inner device is to be arranged with its circumferential support structure within the native valve annulus or at an interior position close thereto and in-between the native valve leaflets, and - an outer device configured to be disposed on the exterior of the connection channel, wherein the outer device is configured to at least partly extend around the inner device at a radial distance to the inner device, and wherein the inner and outer devices (19, 25) are configured to form a securing mechanism for securing the circumferential connection channel wall structure therebetween, wherein the outer device is to be arranged around the exterior of the native valve leaflets close to the valve annulus, the native valve leaflets forming part of the connection channel wall structure, wherein the outer device is configured to form a ring, for extending circumferentially around the circumferential connection channel wall structure, between and at a distance to the axial ends of the inner device, characterized in that the circumferential support structure of the inner device comprises an outer circumferential groove and the ring of the outer device is configured to be aligned to the outer circumferential groove, and wherein the ring is an open or closed ring for engaging the circumferential groove with the connection channel wall structure clamped therebetween and with the corresponding area of the native valve leaflets forced radially into the outer circumferential groove, and in that the inner device has a funnel shape corresponding generally to a funnel shape of the connection channel, wherein the funnel shape is provided at one of the axial ends (21', 21") of the circumferential support member of the inner device, which in implanted condition is proximal to the native valve annulus. - an inner device configured to be disposed in an interior of the connection channel, the inner device having a circumferential support structure which is radially expandable, and having a valve attached to the circumferential support structure, wherein the circumferential support structure of the inner device is of tubular shape and extends along an axis and has two axial ends (21', 21"), wherein the inner device is to be arranged with its circumferential support structure within the native valve annulus or at an interior position close thereto and in-between the native valve leaflets, and - an outer device configured to be disposed on the exterior of the connection channel, wherein the outer device is configured to at least partly extend around the inner device at a radial distance to the inner device, and wherein the inner and outer devices (19, 25) are configured to form a securing mechanism for securing the circumferential connection channel wall structure therebetween, wherein the outer device is to be arranged around the exterior of the native valve leaflets close to the valve annulus, the native valve leaflets forming part of the connection channel wall structure, wherein the outer device is configured to form a ring, for extending circumferentially around the circumferential connection channel wall structure, between and at a distance to the axial ends of the inner device, characterized in that the circumferential support structure of the inner device comprises an outer circumferential groove and the ring of the outer device is configured to be aligned to the outer circumferential groove, and wherein the ring is an open or closed ring for engaging the circumferential groove with the connection channel wall structure clamped therebetween and with the corresponding area of the native valve leaflets forced radially into the outer circumferential groove, and in that the inner device has a funnel shape corresponding generally to a funnel shape of the connection channel, wherein the funnel shape is provided at one of the axial ends (21', 21") of the circumferential support member of the inner device, which in implanted condition is proximal to the native valve annulus. wherein the outer device is configured to form a ring, for extending circumferentially around the circumferential connection channel wall structure, between and at a distance to the axial ends of the inner device, characterized in that the circumferential support structure of the inner device comprises an outer circumferential groove and the ring of the outer device is configured to be aligned to the outer circumferential groove, and wherein the ring is an open or closed ring for engaging the circumferential groove with the connection channel wall structure clamped therebetween and with the corresponding area of the native valve leaflets forced radially into the outer circumferential groove, and in that the inner device has a funnel shape corresponding generally to a funnel shape of the connection channel, wherein the funnel shape is provided at one of the axial ends (21', 21") of the circumferential support member of the inner device, which in implanted condition is proximal to the native valve annulus.