The paper studies controllability problems (exact and approximate) of a class of semilinear parabolic systems in a bounded domain described by
Here, denotes the state; locally Lipschitz continuous; the characteristic function of the nonempty subset ; and the control. Exact controllability of the system is defined as having the following property: Given and (corresponding to and ), there exists a control such that . If is of polynomial growth order and is bounded from above by at infinity, the exact controllability as well as the approximate controllability are guaranteed. Also the existence of behaving like at infinity with such that the system fails to be exactly and approximately controllable is shown.