Abstract: This paper investigates the asymptotic normality of the estimation error of steady-state models of industrial processes in quite mild conditions. The estimate is formed from the estimated parameters of an approximate linear model which is strong consistent to the steady-stategain of the slow time-varying linear SISO system. In the parameter estimation, the weighted leastsquares method is employed. The input signal (the system set point) is the usual step change in the optimization procedure. The rate of convergence is given out in this paper. The stationarity and the distribution of the stochastic process are not demanded. Under some ac- ceptable conditions, the robustness to the structure of the approximate linear model is achieved In simulaion study, it is shown that for limited length of the sampled data, the best choice of the structure of approximate models in the aspect of estimation precision is dependent upon the realization of the stochastic noise.