We consider the problem of synthesizing correct-by-construction globally asynchronous, locally synchronous (GALS) implementations from modular synchronous specifications. This involves the synthesis of asynchronous wrappers that drive the synchronous clocks of the modules and perform input reading in such a fashion as to preserve, in a certain sense, the global properties of the system. Our approach is based on the theory of weakly endochronous systems, which gives criteria guaranteeing the existence of simple and efficient asynchronous wrappers. We focus on the transformation (by means of added signalling) of the synchronous modules of a multiclock synchronous specification into weakly endochronous modules, for which simple and efficient wrappers exist. Categories and Subject Descriptors: D.2.2: CASE General Terms: Algorithms, Reliability, Verification.