This is a joint work with S.C. Power. We define nonselfadjoint operator algebras with generators Le1 , . . . , Len , Lf1 , . . . , Lfm subject to commutation relations given by a unitary mn×mn matrix u. These algebras, which generalize the analytic Toeplitz algebras of rank 2 graphs with a single vertex, are classified up to isometric isomorphism in terms of the unitary matrix u