The paper is devoted to the regularization of ill-posed stochastic Cauchy problems in Hilbert spaces: du (t) = Au (t) dt + Bd W (t), t > 0, u (0) = ζ.(0.1). The need for regularization is connected with the fact that in the general case the operator A is not supposed to generate a strongly continuous semigroup and with the divergence of the series defining the infinite-dimensional Wiener process {W (t): t ≥ 0 }. The construction of regularizing operators uses the technique of Dunford-Schwartz operators, regularized semigroups, generalized Fourier transform and infinite-dimensional Q-Wiener processes.