Abstract: A knee support or replacement apparatus of the asymmetrical multi-convolution type comprising at least one outer joint and one inner joint which are arranged each side of a vertical antero-posterior plane and which each comprise at least one proximal member and at least one distal member articulated together. A first connection device is for connecting together the proximal members and the distal members, and a guide device provides the articulated members, with different movements for each joint. The articulated members of each joint exhibit bearing surfaces with complex curvatures different from each other by means of which they are in only partial contact, at at least three points.