The invention relates to pseudo-peptides according to the formula: ##STR1## wherein R.sup.1 is a group inhibiting an amine function, or an amino acid residue or peptide with an inhibited terminal amino function, R.sup.2 represents the lateral chain of a natural or non-natural amino acid, R.sup.3 represents: 1) the lateral chain of a natural amino acid except for Gly and Ala, not substituted or substituted by an aryl group, 2) an aralkyl group, or 3) an alkyl group comprising at least 3 carbon atoms, and R.sup.4 represents a lateral chain of natural or non-natural amino acid. They are useful as matrix zinc metalloprotease inhibitors, particularly in the treatment of cancer.