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 or related disorders. The method comprises administering to a subject a pharmaceutical composition comprising an effective amount of a non-nucleotide compound, preferably a P2Y.sub.12 receptor antagonist compound, wherein said amount is effective to inhibit platelet aggregation. The compounds useful for this invention include compounds of general Formulae III, IIIa, and IIIb, or salts, hydrates, and solvates thereof. The present invention also provides novel compounds of Formulae IIIa and IIIb, which are potent and have a good oral bioavailability.