The author, basing on the practice of Russian state commercial (arbitrazh) courts published in 2007-2008, analyzes certain aspects of consideration of claims contesting or seeking recognition and enforcement of awards issued in international commercial arbitration, i.a., law and international treaty applicable in the resolution of such category of claims, application by the said courts of the public policy concept, and some other. Published in the International Commercial Arbitration journal, No. 4, 2008.