  We obtain several higher order periodic solutions of a Coupled phi6 model in
terms of Lame polynomials of order one and two. These solutions are unusual in
the sense that while they are the solutions of the coupled problem, they are
not the solutions of the uncoupled problem. We also obtain exact solutions of
coupled phi6-phi4 models, both when the phi4 potential corresponds to a first
order (asymmetric double well) or a second order (symmetric double well)
transition.
