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The continual reachability set, the set of initial states of a constrained dynamical system that can reach a target at any desired time, is introduced. The properties of this set are investigated and its connection with maximal reachability constructs is examined. Owing to this connection, efficient and scalable maximal reachability techniques can be used to compute the continual reachability set. An approximation of this set based on ellipsoidal techniques is presented. The results are demonstrated on a problem of control of anesthesia.