Timing Closure in presence of long global wire interconnects is one of the main current issues in System-onChip design. One proposed solution to the Timing Closure problem is Latency-Insensitive Design (LID) [5,7]. It was noticed in [7] that, in many cases, the dynamically scheduled synchronisations introduced by latency-insensitive protocols could be computed off-line as a static periodic schedule. We showed in [2,3] how this schedule could then be used to further optimize the protocol resources when they are found redundant. The purpose of the present paper is to study how the larger blocks, obtained as synchronous components interconnected by LID protocols optimized by static schedule informations, can be again made to operate with an environment that provides also I/O connections at its own (synchronous or GALS) rate. We also consider the case of multirate SoC, using results from SDF (Synchronous DataFlow) theory [12].