A nonlinear nonstationary regression model has recently attracted increasing attention and includes some interesting models such as binary choice and linear regression (co- integrated). In this talk, we consider the parametric linear single index model with nonstationary regressors. Chang and Park (2001) has also studied this model under the integrable assumption to analyze smooth transition regression and binary choice models. However, the integrable assumption excludes linear regression model, so that this assumption seems restrictive for some applications. Without assuming the integrable assumption, we consider the parameter estimation problem by using the nonlinear least squares estimator.