In this paper we consider certain problems of optimal feedback control of systems governed by a general Ito stochastic differential equation that allows for jumps in tho diffusion process. It will bo shown that these stochastic optimal feedback eontrol problems can be converted into problems of optimal control of deterministic systems described by a parabolic integro-partial-difforential equation. Both tho fixed terminal time and the Markov terminal time problems are converted to optimal control problems of distributed parameter systems with Cauchy condition. However, tho stochastic optimal feedback control problem with Markov terminal time can also bo reduced to the optimal eontrol problem of deterministic systems described by a partial integro-difforcntial equation of parabolic type with the first boundary condition. Further it is interesting to note that tho objective funetionals for all tho reduced problems have precisely the same form.