Peptides (from Gr. πεπτός, digested, derived from πέσσειν, to digest) are biologically occurring short chains of amino acid monomers linked by peptide (amide) bonds. The covalent chemical bonds are formed when the carboxyl group of one amino acid reacts with the amino group of another.mino acids that have been incorporated into peptides are termed residues due to the release of either a hydrogen ion from the amine end or a hydroxyl ion from the carboxyl end, or both, as a water molecule is released during formation of each amide bond.