Acylpeptides derived from somatostatin or from a derivative thereof having analogous action, in which the amino acids sequence is modified by omitting individual amino acids and/or by exchanging them for other amino acids, and in which the .epsilon.-amino group of the lysine residue in the 9-position, and optionally also the .epsilon.-amino group of the lysine residue in the 4-position and/or the N-terminal .alpha.-amino group carries the acyl radical of an optionally substituted alkanecarboxylic acid, and salts and complexes thereof can be used as antidiabetics and/or for combating gastrointestinal bleeding. They are manufactured by conventional methods of peptide chemistry.