The invention provides cyclic peptides which inhibit platelet aggregation without causing prolonged bleeding time. The invention provides RGD or KGD containing peptides which are cyclized and contain hydrophobic moieties adjacent to the carboxy terminus of the RGD sequence. Peptides of this nature are also provided which contain in addition to the hydrophobic. moiety an adjacent positively charged moiety. Such peptides have a high affinity for the receptor IIb/IIIa and a low affinity for the fibronectin and vitronectin receptors. Such peptides can be administered in a suitable physiologically acceptable carrier to therapeutically treat thrombosis.