This paper studies identification of systems with input nonlinearities of known structure. For input nonlinearities parameterized by one parameter, a deterministic approach is proposed based on the idea of separable least squares. The identification problem is shown to be equivalent to an one-dimensional minimization problem. The method is very effective for several common static and non-static input nonlinearities. For a general input nonlinearity, a correlation analysis based identification algorithm is presented which is shown to be convergent.