  We consider a random process as a solution of stochastic differential
equations with dependence of the coefficients on small parameter $\varepsilon$
and we suppose that the drift coefficients of these equations are unbounded on
the parameter $\varepsilon$. We consider more general requirements on the
convergence of some functions of coefficients of stochastic equations to limit
functions. Necessary and sufficient conditions for the weak convergence of
solutions of such stochastic equations if $\varepsilon$ tends to zero to a some
stochastic equations involving a local time of process are obtained.
