An algebra A of finite similarity type \(\Omega\) containing neither nullary nor unary operations is said to be nilpotent iff it satisfies the identities \(u=v\) for all ”sufficiently long” words u and v. A variety is nilpotent iff it consists of nilpotent algebras. The main result is as follows: For any varieties \({\mathfrak M}\) and \({\mathfrak N}\) of type \(\Omega\) if \({\mathfrak N}\) is nilpotent then the variety \({\mathfrak M}\vee {\mathfrak N}\) is finitely based iff \({\mathfrak M}\) is finitely based.