Conditions for polymorphism at pleiotropic loci with antagonistic effects on fitness components are investigated, under the assumptions of additivity and multiplicativity of fitness components. We show that the conditions for stable polymorphism are rather restrictive, especially with weak selection. The conditions are also very sensitive to the dominance parameters; in particular, reversal of dominance is often required for stable polymorphism. A review of biochemical mechanisms of dominance suggests that dominance reversal is not likely to be common. The conditions for maintaining genetic variation at two antagonistic and pleiotropic loci are even more restrictive than for the one-locus case. When conditions for stable polymorphism by antagonistic pleiotropy are satisfied, substantial dominance variance in one or both fitness components is expected but is seldom observed in experiments. Antagonistic pleiotropy implies stabilizing selection on the fitness components separately, which usually tends to red...