Consider an infinite chain of particles subjected to a potential f, where nearest neighbours are connected by nonlinear oscillators. The nonlinear coupling between particles is given by a potential V. The dynamics of the system is described by the infinite system of second order differential equations

<(q)double over dot>(j) + f'(q(j)) = V'(q(j+1) - q(j)) - V'(q(j) - q(j-1)), j is an element of Z.

We investigate the existence of travelling wave solutions. Two kinds of such solutions are studied: periodic and homoclinic ones. On one hand, we prove under some growth conditions on f and V, the existence of non-constant periodic solutions of any given period T > 0, and speed c > c(0), where the constant c(0) depends on f ''(0) and V ''(0). On the other hand, under very similar conditions, we establish the existence of non-trivial homoclinic solutions, of any given speed c > c(0), emanating from the origin. Moreover, we prove that these homoclinics decay exponentially at infinity. Each homoclinic is obtained as a limit of periodic solutions when the period goes to infinity. (C) 2010 Elsevier Ltd. All rights reserved.