The long-term population genetics of multigene families is influenced by several biased and unbiased mechanisms of nonreciprocal exchanges (gene conversion, unequal exchanges, transposition) between member genes, often distributed on several chromosomes. These mechanisms cause fluctuations in the copy number of variant genes in an individual and lead to a gradual replacement of an original family of n genes (A) in N number of individuals by a variant gene (a). The process for spreading a variant gene through a family and through a population is called molecular drive. Consideration of the known slow rates of nonreciprocal exchanges predicts that the population variance in the copy number of gene a per individual is small at any given generation during molecular drive. Genotypes at a given generation are expected only to range over a small section of all possible genotypes from one extreme (n number of A) to the other (n number of a). A theory is developed for estimating the size of the population variance by using the concept of identity coefficients. In particular, the variance in the course of spreading of a single mutant gene of a multigene family was investigated in detail, and the theory of identity coefficients at the state of steady decay of genetic variability proved to be useful. Monte Carlo simulations and numerical analysis based on realistic rates of exchange in families of known size reveal the correctness of the theoretical prediction and also assess the effect of bias in turnover. The population dynamics of molecular drive in gradually increasing the mean copy number of a variant gene without the generation of a large variance (population cohesion) is of significance regarding potential interactions between natural selection and molecular drive.