In a previous publication (1983), we defined a class of algebras, denoted by MS, which generalises both de Morgan algebras and Stone algebras. Here we describe the lattice of subvarieties of MS. This is a 20-element distributive lattice. We then characterise all the subvarieties of MS by means of identities. We also show that some of these subvarieties can be described in terms of three important subsets of the algebra. Finally, we determine the greatest homomorphic image of an MS-algebra that belongs to a given subvariety.