Compounds of formula (I): 1 wherein: X.sub.1 represents an atom or group selected from CR.sub.4aR.sub.4b, O, S(O).sub.q1 and NR.sub.5, wherein R.sub.4a, R.sub.4b, q.sub.1 and R.sub.5 are as defined in the description, m.sub.1 represents zero or an integer from 1 to 4 inclusive, m.sub.2 represents an integer from 1 to 4 inclusive, n.sub.1 and n.sub.2, which may be identical or different, each represent an integer from 1 to 3 inclusive, R.sub.1 represents hydrogen or a group selected from carboxy, alkoxycarbonyl, optionally substituted carbamoyl and optionally substituted alkyl, R.sub.2 represents hydrogen or alkyl, Ak represents an optionally substituted alkylene chain, p represents zero, 1 or 2, R.sub.3 represents hydrogen or cyano, X.sub.2 and X.sub.3, which may be identical or different, each represent either S(O).sub.q2, or CR.sub.6aR.sub.6b, wherein q.sub.2, R.sub.6a and R.sub.6b are as defined in the description, its optical isomers, where they exist, and its addition salts with a pharmaceutically acceptable acid. Medicinal products containing the same which are useful as DPP-IV inhibitors.