The adaptive value of epigenetic inheritance systems is investigated in a simple mathematical framework. These systems enable the environmentally induced phenotypes to be transmitted between generations. The frequencies of the different epigenetic variants are determined by the plasticity and the efficiency of transmission (called memory). Plasticity and memory are genetically determined. This paper studies the evolution of a quantitative character, its plasticity and memory, on the adaptive landscape. Due to the dual inheritance of the character, selection acts on two levels: on the phenotypes of the same genotype, and on the different genotypes. Plasticity generates the raw material, and memory increases the strength of phenotypic selection. If the character is far from the peak of the landscape, then dual inheritance of the character can be advantageous for the genotype. Near the peak it is more favourable to suppress phenotypic variation. This would lead to genetic assimilation.