Mitral or tricuspid heart valve prosthesis, comprising an expandable tubular frame and a prosthetic valve mounted on the frame, said frame comprising an atrial portion, intended to be placed at the atrium of a heart, a ventricular portion intended to be placed at the ventricle of a heart, and an annular portion situated between these atrial and ventricular portions and intended to be placed at the native valve annulus; - said atrial portion is made up of three or four metal-wire extensions, regularly distributed on the circumference of this atrial portion and projecting from said annular portion, each extension being made up of a single upside-down U-shaped or V-shaped wire, characterized in that: - extensions developing with a curved shape such that in the expansion state of the prosthesis, the base of this extension is oriented radially toward the outside of said annular portion, then the extension curves toward the inside of the frame, such that the various extensions are substantially part of an imaginary truncated sphere placed above said annular portion and are arranged to provide bearing against an atrial part of the valve annulus and against the adjacent wall of the atrium; - said annular portion is made up of diamond meshes connected to one another by their corners, which comprise anchoring points protruding from its outer face, in which the anchoring points are arranged to be inserted into the valve annulus; and - said ventricular portion is made up of three or four metal-wire extensions, regularly distributed on the circumference of this ventricular portion and projecting from said annular portion, each extension being made up of a single U-shaped or V-shaped wire and developing with a curved shape such that in the expansion state of the prosthesis, the base of this extension is oriented radially toward the outside of said annular portion, then the extension curves toward the inside of the frame, such that the various extensions are substantially part of an imaginary ovoid placed below said annular portion, and are arranged to closely apply against the ventricular part of the valve annulus and are well suited to the shape of the ventricle. - said atrial portion is made up of three or four metal-wire extensions, regularly distributed on the circumference of this atrial portion and projecting from said annular portion, each extension being made up of a single upside-down U-shaped or V-shaped wire, - extensions developing with a curved shape such that in the expansion state of the prosthesis, the base of this extension is oriented radially toward the outside of said annular portion, then the extension curves toward the inside of the frame, such that the various extensions are substantially part of an imaginary truncated sphere placed above said annular portion and are arranged to provide bearing against an atrial part of the valve annulus and against the adjacent wall of the atrium; - said annular portion is made up of diamond meshes connected to one another by their corners, which comprise anchoring points protruding from its outer face, in which the anchoring points are arranged to be inserted into the valve annulus; and - said ventricular portion is made up of three or four metal-wire extensions, regularly distributed on the circumference of this ventricular portion and projecting from said annular portion, each extension being made up of a single U-shaped or V-shaped wire and developing with a curved shape such that in the expansion state of the prosthesis, the base of this extension is oriented radially toward the outside of said annular portion, then the extension curves toward the inside of the frame, such that the various extensions are substantially part of an imaginary ovoid placed below said annular portion, and are arranged to closely apply against the ventricular part of the valve annulus and are well suited to the shape of the ventricle.