Template-fixed β-hairpin mimetics and libraries including a plurality of these mimetics are provided. The template-fixed β-hairpin mimetics are of the following general formula: R1-Cys-Z-Cys-R2  (I) wherein the two cysteine residues are bridged by a disulfide bond, thereby forming a cyclic peptide; R1 and R2 are di- or tripeptide moieties of certain types, as defined herein; and Z is a chain of n amino acid residues with n being an integer from 4 to 20 and with each of these n amino acid residues being, independently, derived from any naturally occurring L-α-amino acid.