Hypotheses of homology are the basis of comparative morphology and comparative molecular biology. The kinds of homologous and nonhomologous relations in classical and molecular biology are explored through the three tests that may be applied to a hypothesis of homology: congruence, conjunction, and similarity. The same three tests apply in molecular comparisons and in morphology, and in each field they differentiate eight kinds of relation. These various relations are discussed and compared. The unit or standard of comparison differs in morphology and in molecular biology; in morphology it is the adult or life cycle, but with molecules it is the haploid genome. In morphology the congruence test is decisive in separating homology and nonhomology, whereas with molecular sequence data similarity is the decisive test. Consequences of this difference are that the boundary between homology and nonhomology is not the same in molecular biology as in morphology, that homology and synapomorphy can be equated in morphology but not in all molecular comparisons, and that there is no detected molecular equivalent of convergence. Since molecular homology may reflect either species phylogeny or gene phylogeny, there are more kinds of homologous relation between molecular sequences than in morphology. The terms paraxenology and plerology are proposed for two of these kinds--respectively, the consequence of multiple xenology and of gene conversion.