The aim of the present paper is to investigate the solution of the stochastic hereditary integrodifferential equation of It type with “small” perturbations which is at least a non-Markovian process, by comparing it with the solution of a simpler equation, i.e. of an unperturbed stochastic hereditary differential equation the solution of which is certainly a Markovian process. More precisely, we estimate the closeness of the (2m)th moments of these solutions. If the solutions are defined on unbounded intervals, we give sufficient conditions under which they are closed on intervals whose length goes to infinity.