The present invention relates to a compound of general formula (I) below: Signal−Linker−Peptide (I) in which Signal represents a signal entity; Linker, which may or may not be present, represents a chemical bond and Peptide represents a peptide comprising an apoptosis-targeting peptide, the apoptosis-targeting peptide being chosen from the peptides having the formula below and the functional equivalents thereof: X1-X2-X3-X4-X5-X6 (1) (SEQ ID No 1) in which X1 and X2 represent, independently of one another, leucine or isoleucine, X3 and X4 represent lysine, X5 represents proline and X6 represents phenylalanine, advantageously the peptide L-I-K-K-P-F (SEQ ID No 11) and the functional equivalents thereof; D-A-H-S-X7-S (2) (SEQ ID No 2) in which X7 represents phenylalanine or leucine; P-G-D-L-X8-X9 (3) (SEQ ID No 3) in which X8 represents serine or valine and X9 represents threonine or arginine; H-G-X10-L-S-X11 (4) (SEQ ID No 4) in which X10 represents aspartic acid or histidine, and X11 represents threonine or isoleucine; V-L-G-E-R-G (5) (SEQ ID No 5); and the pharmaceutically acceptable salts of these compounds.