This invention is directed to a method of preventing or treating diseases or conditions associated with platelet aggregation. The method is also directed to a method of treating thrombosis. The method comprises administering to a subject a pharmaceutical composition comprising a therapeutically effective amount of P2Y.sub.12 receptor antagonist compound, wherein said amount is effective to bind the P2Y.sub.12 receptors on platelets and inhibit ADP-induced platelet aggregation. The P2Y.sub.12 receptor antagonist compounds useful for this invention include mononucleoside polyphosphates and dinucleoside polyphosphates of general Formula I, or salts thereof The present invention also provides compositions comprising mononucleoside polyphosphates and dinucleoside polyphosphates according to Formula Ia and Ib.