Cyclic peptides of the formula ##STR1## in which trp represents L-Trp, D-Trp, or an analogous radical which carries a halogen atom in the indole nucleus, Ac.sub.A represents hydrogen, or an acyl radical Ac of a carboxylic acid present at the .epsilon.-amino group, A represents L-Phe, D-Phe, L-Phg or D-Phg, or a corresponding radical having a substituted or saturated phenyl ring, and B represents the residue of a .gamma.- or .delta.-amino-lower alkanecarboxylic acid which may carry an optionally substituted cyclic hydrocarbyl radical Ar, and also pharmacologically tolerable salts and therapeutically acceptable complexes thereof can be used as an antidiabetic in an analogous manner to somatostatin. They can be obtained by conventional processes of peptide chemistry, especially by cyclisation of corresponding linear peptides.