Abstract The natural su( N) generalization of the XX model is introduced and analyzed. It is defined in terms of the characterizing properties of the usual XX model: the existence of two infinite sequences of mutually commuting conservation laws and the existence of two infinite sequences of mastersymmetries. The integrability of these models, which cannot be obtained in a degenerate limit of the su( N) XXZ model, is established in two ways: by exhibiting their R matrix and from a direct construction of the commuting conservation laws. We then diagonalize the conserved laws by the method of the algebraic Bethe ansatz. The resulting spectrum is trivial in a certain sense; this provides another indication that the XX su( N) model is the natural generalization of the su(2) model. The application of these models to the construction of an integrable ladder, that is, an su( N) version of the Hubbard model, is mentioned.