The invention concerns a medicine comprising, as active principle, an efficient quantity of at least an oligosaccharide substance capable of modulating apoptosis dysfunction which is capable of modifying apoptosis dysfunctions said substance being selected from the group consisting of oligosaccharides which are derived, by enzymatic or chemical process, from the polymers of the group comprising (1→3)-&bgr;-glucans which optionally comprise (1→6)-&bgr;-branching, and oligosaccharides which are derived, by enzymatic or chemical process, from sulfated galactans, it also concerns a method for treating apoptosis dysfunction.