Summary: An analytic study on a complex nonlinear system (Coupled Higgs equation) and a nonlinear variant of the PHI-four equation is presented in this paper. The Exp-function method is employed to derive exact periodic and generalized solitary solutions of these equations. The solutions are compared with those obtained by the tanh method, the sine-cosine method and the Weierstrass elliptic function method, furthermore, new and more general solutions are found.