The exp［-φ(ξ)］-expansion method can be used to solve the nonlinear evolution equation with variable coefficients. By taking the generalized variable coefficient KdV-mKdV equation and variable coefficient (2+1)-dimensional Broer-Kaup equations as an example, the solving process is realized and singular travelling wave solutions are obtained, which are expressed in terms of the exponential functions, hyperbolic functions, trigonometric functions and rational functions. When parameters are taken to be special values, the kink type solitary wave solutions are derived. It is shown that the exp［-φ(ξ)］-expansion method is suitable for solving the nonlinear evolution equations with variable coefficients, and it is more general.