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We provide a small-gain theorem for feedback interconnections of monotone input-output systems with multi-valued input-state characteristics. This extends a small-gain theorem of Angeli and Sontag for monotone systems with singleton-valued characteristics. We prove our theorem using Thieme's convergence theory for asymptotically autonomous systems. We also provide an illustrative example.

A small-gain theorem for motone systems with multivalued input-state characteristics