Time-optimal control of axial xenon oscillations in pressurized water reactors is investigated in the present study, properly accounting for operating constraints on the allowable axial offset (AO) band. The system equation describing the spatial xenon oscillations has been reformulated using a lambda mode expansion in a form that readily allows a physical interpretation of the state vector and the system equation. In particular, AO measurements can be used to define the entire system parameters completely. Previous optimal control studies have been limited to the case of controls to the origin in the xenon-iodine phase plane. Our present investigation indicates that time-optimal controls should, in general, involve bang-bang controls to a line segment in this phase plane, subject to a band constraint on allowable AO or available control strength. A suboptimal control strategy, which can be applied directly in actual operating conditions without the aid of on-line computers, is also proposed. Verification of the proposed time-optimal control strategies is performed through computer simulations of xenon-induced transients.