This chapter proposes a simple replicator theory of the coevolution of genes and memes. The presented coevolutionary theory assumes that units of information acquired from parents by imitation (memes) are not independent of genes, but are obligatorily bounded with genes as composites, which are subjects of Darwinian evolution. A population composed of couples of genes and memes, the so-called m-genes, is postulated as a subject of Darwinian evolution. Three different types of operations over m-genes are introduced: replication (an m-gene is replicated with mutations onto an offspring m-gene), interaction (a memetic transfer from a donor to an acceptor), and extinction (an m-gene is eliminated). Computer simulations of the present model allow us to identify different mechanisms of gene and meme coevolutions.