In higher plants, animals and fungi, there are two inheritance systems: the familiar system, depending on DNA sequence, used in transmitting information between sexual generations, and an epigenetic inheritance system, depending on gene activation, responsible for the transmission of states of differentiation during development. Occasionally, epigenetic changes are transmitted in sexual reproduction. A formal model of such a dual inheritance system is presented, and it is shown how the separation between the two systems can sometimes break down. The evolutionary significance of such breakdowns is discussed.