  The integrability of the N-cosine model, a N-field generalization of the
sine-Gordon model, is investigated. We establish to first order in conformal
perturbation theory that, for arbitrary N, the model possesses a quantum
conserved current of Lorentz spin 3 on a submanifold of the parameter space
where the interaction becomes marginal. The integrability of the model on this
submanifold is further studied using renormalization techniques. It is shown
that for N = 2, 3, and 4 there exist special points on the marginal manifold at
which the N-cosine model is equivalent to models of Gross-Neveu type and
therefore is integrable. In the 2-field case we further argue that the points
mentioned above exhaust all integrable cases on the marginal submanifold.
