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This paper addresses the stability of traffic flow on a highway when the vehicles operate under an adaptive cruise-control (ACC) system. These systems are commonly designed to maintain a constant time gap between vehicles during vehicle following. Previous researchers in the literature have produced contradictory results on whether the traffic flow is stable when the constant time-gap spacing policy is used. This paper resolves the contradiction and shows that the boundary conditions used at the inlets and exits influence traffic-flow stability in the case of the constant time-gap policy. Further, this paper shows that it is possible to design an unconditionally stable spacing policy, i.e., a spacing policy that guarantees traffic stability under all boundary conditions. The practical implications of instability are shown through traffic-simulation results. The advantages of an unconditionally stable spacing policy over the constant time-gap policy are demonstrated. The answer to the question "Should ACC systems be designed to maintain a constant time gap between vehicles?" is "No" from a traffic-flow stability perspective. It is quite easy to develop alternate spacing policies with superior stability properties.