The present invention relates to peptidomimetics capable of inhibiting CD28 and/or CTLA-4 interaction with CD80 (B7-1) and CD86 (B7-2) and having a core amino acid sequence, LeuMetTyrProProProTyrTyr, corresponding to residues 2 to 9 of SEQ ID NO:1. The present invention also relates to pharmaceutical compositions and a method of treating pathologies and disorders which are improved by inhibition of CD28 and/or CTLA-4 interaction with CD80 and CD86.