The main purpose of this paper is to weak requirements in a theorem of Has'minski\u i [2]. The asymptotic behaviour of the solution$X_{\varepsilon}(t,\omega)$of equation (0.1) as$\varepsilon\to 0$is studied. The main assumptions are the following: conditions (1.1) and (1.2) are fulfilled, the processes$F^{(i)}(x,t,\omega)$satisfy Kolmogorov's mixing condition (0.4) (for a special type of processes$F^{(i)}$, see condition (4'), Rosenblatt's mixing condition (0.3) is sufficient), limits (1.4) and (1.5) exist. Under these assumptions and some additional ones the process$X_{\varepsilon}(\tau/\varepsilon^2,\omega)$is proved to converge weakly to a Markov process$X_0(\tau,\omega)$. The local characteristics of$X_0(\tau,\omega)$are calculated from condition (1.5).