Two different processes contribute to mutation accumulation in finite populations: fixation of mutant alleles and Muller's ratchet. In very small random-mating populations, and with tight linkage, fixation of mutant alleles occurs at a high rate. With very restricted recombination, the number of low-frequency mutant alleles per genome in random-mating populations also increases over time independently of fixation (Muller's ratchet). Increased population size affects the ratchet less than the fixation process, and the decline in population fitness is dominated by the ratchet in populations of size greater than about 100, especially with high mutation rates. Neither fixation nor the ratchet has serious effects unless recombination is severely restricted. The effects of differences in the selection parameters (strength of selection, dominance coefficient) can be interpreted in terms of opposing effects of selection, on individual loci and associations between loci. Stronger selection slows the accumulation of mutations, although a faster decline in mean fitness sometime results. Increasing the dominance coefficients of the mutant alleles tends to act similarly. High inbreeding slows the ratchet, because with homozygosity there is a higher initial frequency of the least loaded class, as the increased homozygous expression of mutant alleles in inbred populations has effects similar to stronger selection. Fixation of mildly deleterious mutations is accelerated in highly inbred populations, but fitness decline due to mutation accumulation was rapid only in very small populations and was always much slower than for asexual populations. The effects of breeding system and rate of recombination on the rate of molecular evolution by the fixation of slightly deleterious alleles are discussed.