  We define nonselfadjoint operator algebras with generators $L_{e_1},...,
L_{e_n}, L_{f_1},...,L_{f_m}$ subject to the unitary commutation relations of
the form \[ L_{e_i}L_{f_j} = \sum_{k,l} u_{i,j,k,l} L_{f_l}L_{e_k}\] where $u=
(u_{i,j,k,l})$ is an $nm \times nm$ unitary matrix. These algebras, which
generalise the analytic Toeplitz algebras of rank 2 graphs with a single
vertex, are classified up to isometric isomorphism in terms of the matrix $u$.
