There are two major theories of properties that employ resemblance classes to avoid commitment to universals.1 Object-resemblance nominalism ~ORN! faces the notorious companionship and imperfect community difficulties, though some costly remedies have been proposed. Trope-resemblance nominalism ~TRN!, in contrast, is commonly supposed to avoid these difficulties altogether. My contention is that both versions of resemblance nominalism are subject to companionship and imperfect community difficulties. If I am right, ~1! trope theory loses one of its primary selling points, and ~2! resemblance nominalists of either type must appeal to the troublesome remedies that I discuss below.