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We consider the design of an spectrum overlay network where secondary users detect, track, and exploit spectrum opportunities in unslotted primary systems. We develop a decision-theoretic framework for the optimal joint design of the spectrum sensor and tracking and access strategies, and obtain structural solutions. Our results suggest the equivalence between the design of overlay networks in unslotted primary systems and that in slotted primary systems where channel occupancy by primary users can only change at known and fixed time instants. This equivalence points to the possibility of reducing the design of spectrum overlay in unslotted primary systems to that in slotted primary systems, a significantly simpler problem, and porting results available on the latter to the former.