  In this paper we present sufficient conditions for the existence of
heteroclinic or homoclinic solutions for second order coupled systems of
differential equations on the real line. We point out that it is required only
conditions on the homeomorphisms and no growth or asymptotic conditions are
assumed on the nonlinearities. The arguments make use of the fixed point
theory, L^1-Carath\'eodory functions and Schauder's fixed point theorem. An
application to a family of second order nonlinear coupled systems of two
degrees of freedom, shows the applicability of the main theorem.
