A method for total replacement of an affected intervertebral disc through a dorsal approach comprising the steps of removing the disc material of the affected intervertebral disc (3) and inserting an intervertebral prosthesis (30) into the intervertebral disc space via an extraforaminal path (23). An intervertebral prosthesis (100), in particular an intervertebral disk prosthesis comprising A) a first prosthetic component (101) having a first apposition surface (107) disposed transversely to the central axis (103) B) a second prosthetic component (102) having a second apposition surface (108) disposed transversely to the central axis (103); whereby C) said first and second prosthetic components (101;102) are connected by means of an articulation (106); whereby D) when viewed parallel to said central axis (103) said first and second prosthetic components (101;102) have an elongated shape with a major axis (127) and a transverse minor axis (128); E) said central axis (103), major axis (127) and transverse minor axis (128) intersecting each other and said central axis (103) and transverse minor axis (128) defining a middle plane (126); F) said first and second prosthetic component (101;102) have a cross-sectional area orthogonal to said central axis (103) which is essentially oval or elliptical; whereby G) said cross-sectional area comprises at least two concavities (125;130) lying on different sides of said middle plane (126) and on the same side of said major axis (127).