Classification of fats and oils involves the recognition of one/several markers typical of the product. The ideal marker(s) should be specific to the fat or oil. Not many chemical markers fulfill these criteria. Authenticity assessment is a difficult task, which in most cases requires the measurement of several markers and must take into account natural and technology-induced variation. The present study focuses on the identity prediction of three by-products of the fat industry (animal fats, fish oils, recycled cooking oils), which may be used for animal feeding. Their identities were predicted by their triacylglycerol fingerprints, their fatty acid fingerprints and their profiles of volatile organic compounds. Partial least square discriminant analysis allowed samples to be assigned successfully into their identity classes. Most successful were triacylglycerol and fatty acid fingerprints (both 96% correct classification). Proton transfer reaction mass spectra of the volatile compounds predicted the identity of the fats in 92% of the samples correctly.