The authors investigate the following semilinear controlled equation with delay in a Hilbert space:
where is a Hilbert space-valued Wiener process, generates an analytic semigroup and , are functions on the path space, . The basic space is the domain of the fractional power operator . It is proved that under Lipschitz and growth conditions on , , approximate controllability of the deterministic system implies approximate controllability of the stochastic one (i.e., the -closure of possible values of , as varies, is the whole , being related to ). A criterion of exact controllability is also given (the assumption on the compactness of the semigroup is then dropped). Finally, an application to a stochastic heat equation is shown.