A nonlinear nonstationary regression model has attracted increasing attention. This model is often modeled as parametric or nonparametric one. The parametric model needs prior knowledge about functional form. Though the nonparametric model does not assume prior functional form information, the number of the regressors must be restricted to be one or two by the technical reason to develop asymptotic theory. This talk proposes the single-index model that does not need prior knowledge about functional form and allows the arbitrary number of the regressors. Since this model includes various models such as cointegration, probit and logit ones, this model can be applied to various empirical studies. We apply the semiparametric least squares (SLS) estimation techniques proposed by Ichimura(1993) to the single-index model with the nonstationary regressors and derive consistency and asymptotic distribution of the SLS estimator.