It is now known that many multigene and supergene families exist in eukaryote genomes: multigene families with uniform copy members like genes for ribosomal RNA, those with variable members like immunoglobulin genes, and supergene families such as those for various growth factor and hormone receptors. Many such examples indicate that gene duplication and subsequent differentiation are extremely important for organismal evolution. In particular, gene duplication could well have been the primary mechanism for the evolution of complexity in higher organisms. Population genetic models for the origin of gene families with diverse functions are presented, in which natural selection favors those genomes with more useful mutants in duplicated genes. Since any gene has a certain probability of degenerating by mutation, success versus failure in acquiring a new gene by duplication may be expressed as the ratio of probabilities of spreading of useful versus detrimental mutations in redundant gene copies. Also examined are the effects of gene duplication on evolution by compensatory advantageous mutations. Results of the analyses show that both natural selection and random drift are important for the origin of gene families. In addition, interaction between molecular mechanisms such as unequal crossing-over and gene conversion, and selection or drift is found to have a large effect on evolution by gene duplication.Key words: gene duplication, gene family, evolution of new genes.