A version of the input-to-output stability (IOS) small gain theorem is derived for interconnections where the subsystems communicate asynchronously over multiple channels, and the communication is subject to multiple time-varying possibly unbounded communication delays. It is shown that a "multi-channel" version of the small gain condition guarantees the stability of the interconnection of IOS subsystems under certain mild assumptions imposed on communication process. The fulfillment of these assumptions does not depend on characteristics of the communication channels, but can always be guaranteed by implementation of certain features of the underlying communication protocol. This result is applicable to a wide range of dynamical systems whose parts communicate over networks, such as Internet-based teleoperators.