The present invention relates to specific inhibitors of the cysteine protease dipeptidyl peptidase I (DP I), which can be used in the treatment of malignant cell degeneration, immune deseases impaired wound healing and metabolic diseases of humans and are represented by the general formula in which R is a peptide or a branched or unbranched C1-C9 alkyl chain, a branched or unbranched C2-C9 alkenyl chain, a branched or unbranched C2-C9 alkynyl chain, a C3-C9 cycloalkyl, C4-C9 carbocyclic, C5-C14 aryl, C3-C9 heteroaryl, C3-C9 heterocyclic, all of the above residues optionally being substituted, the residue AS—AS is a dipeptide or a mimetic thereof, AS is an amino acid or a peptide mimetic thereof. The amino acid is peptide bound with R and R′ is a branched or unbranched C1-C9 alkyl chain, a branched or unbranched C2-C9 alkenyl chain, a branched or unbranched C2-C9 alkynyl chain, a C3-C9 cycloalkyl, C4-C9 cycloalkenyl, C2-C9 heterocycloalkyl, C3-C9 heterocycloalkenyl, C5-C14 aryl, C3-C9 heteroaryl, C3-C9 heterocyclic, whereas the heterocycloalkyl, heterocycloalkenyl, heteroaryl, heterocyclic residue can have up to 6 hetero ring atoms, an amino acid or a peptide mimetic thereof, all of the above residues may be optionally substituted, or is H.