We identify a network of sequential processes that communicate by synchronizing frequently on common actions. More precisely, we demand that there is a bound k such that if the process p executes k steps without hearing from process q---directly or indirectly---then it will never hear from q again. The non-interleaved branching time behavior of a system of connectedly communicating processes (CCP) is given by its event structure unfolding. We show that the monadic second order (MSO) theory of the event structure unfolding of every CCP is decidable. Using this result, we also show that an associated distributed controller synthesis problem is decidable for linear time specifications that do not discriminate between two different linearizations of the same partially ordered execution.