The paper is concerned with solutions of Cauchy's problem for stochastic differential-operator equations in separable Hilbert spaces. Special emphasis is placed on the case when the operator coefficient of the equation is not a generator of a C-0-class semigroup, but rather generates some regularized semigroup. Regularized solutions of equations in the Ito form with a Wiener process as an inhomogeneity and generalized solutions of equations with white noise are constructed in various spaces of abstract distributions.