We present nine diallelic models of genetic conflict in which one allele is imprintable and the other is not to examine how genomic imprinting may have evolved. Imprinting is presumed to be either maternal (i.e., the maternally derived gene is inactivated) or paternal. Females are assumed to be either completely monogamous or always bigamous, so that we may see any effect of multiple paternity. In contrast to previous verbal and quantitative genetic models, we find that genetic conflicts need not lead to paternal imprinting of growth inhibitors and maternal imprinting of growth enhancers. Indeed, in some of our models--those with strict monogamy--the dynamics of maternal and paternal imprinting are identical. Multiple paternity is not necessary for the evolution of imprinting, and in our models of maternal imprinting, multiple paternity has no effect at all. Nevertheless, multiple paternity favors the evolution of paternal imprinting of growth inhibitors and hinders that of growth enhancers. Hence, any degree of multiple paternity means that growth inhibitors are more likely to be paternally imprinted, and growth enhancers maternally so. In all of our models, stable polymorphism of imprinting status is possible and mean fitness can decrease over time. Neither of these behaviors have been predicted by previous models.