Introducing a new genetic model called the discrete allelic-state model, the evolutionary change of genetic variation of quantitative characters within and between populations is studied under the assumption of no selection. This model allows us to study the effects of mutation and random genetic drift in detail. It is shown that when the allelic effects on phenotype are additive, the rate of approach of the genetic variance within populations to the equilibrium value depends only on the effective population size. It is also shown that the distribution of genotypic value often deviates from normality particularly when the effective population size and the number of loci concerned are small. On the other hand, the interpopulational variance increases linearly with time, if the intrapopu-lational variance remains constant. Therefore, the ratio of interpopulational variance to intrapopulational variance can be used for testing the hypothesis of neutral evolution of quantitative characters.