Many enzymes in intermediary metabolism manifest saturation kinetics in which flux is a concave function of enzyme activity and often of the Michaelis-Menten form. The result is that, when natural selection favors increased enzyme activity so as to maximize flux, a point of diminishing returns will be attained in which any increase in flux results in a disproportionately small increase in fitness. Enzyme activity ultimately will reach a level at which the favorable effect of an increase in activity is of the order 1/(4N_e) or smaller, where N_e is the effective population number. At this point, many mutations that result in small changes in activity will result in negligible changes in fitness and will be selectively nearly neutral. We propose that this process is a mechanism whereby conditions for the occurrence of nearly neutral mutations and gene substitutions can be brought about by the long-continued action of natural selection. Evidence for the hypothesis derives from metabolic theory, direct studies of flux, studies of null and other types of alleles in Drosophila melanogaster and chemostat studies in Escherichia coli. Limitations and complications of the theory include changes in environment or genetic background, enzymes with sharply defined optima of activity, overdominance, pleiotropy, multifunctional enzymes and branched metabolic pathways. We conclude that the theory is a useful synthesis that unites many seemingly unrelated observations. The principal theoretical conclusion is that the conditions for the occurrence of neutral evolution can be brought about as an indirect result of the action of natural selection.