The purpose of this paper is to study questions regarding controllability for the distributed-parameter systems described by partial differential equations of parabolic type. Fattorini [2]–[4] studied controllability by finitely many functions of time. We also consider this type of controllability for the distributed-parameter systems with control functions appearing in the differential equations as well as in the boundary conditions. Necessary and sufficient conditions for controllability are presented. We give some useful results for designing controllers which make systems controllable. Several examples are worked out.