A model based on DNA methylation is proposed to explain the initiation and maintenance of mammalian X inactivation and certain aspects of other permanent events in eukaryotic cell differentiation. A key feature of the model is the proposal of sequence-specific DNA methylases that methylate unmethylated sites with great difficulty but easily methylate half-methylated sites. Although such enzymes have not yet been detected in eukaryotes, they are known in bacteria. An argument is presented, based on recent data on DNA-binding proteins, that DNA methylation should affect the binding of regulatory proteins. In support of the model, short reviews are included covering both mammalian X inactivation and bacterial restriction and modification enzymes.