Abstract: It has been studied in this paper that a control of distributed parameter systems is contained in coefficients of linear 2nd order elliptic or parabolic equations, which has been called the problem of control in the coefficients and applied to a numcer of mathemaitcal physics problems. We first give a sufficient condition under which the systein state depends continuously on the control. And then we give conditions respectively for the systems governed by the mentioned equations. Under anyone of them the system has the optimal control minimizing the given cost functional.