A Gaifman-Shapiro-style architecture of program modules is introduced in the case of normal logic programs under stable model semantics. The composition of program modules is suitably limited by module conditions which ensure the compatibility of the module system with stable models. The resulting module theorem properly strengthens Lifschitz and Turner’s splitting set theorem [17] for normal logic programs. Consequently, the respective notion of equivalence between modules, ie modular equivalence, proves to be a congruence relation. Moreover, it is shown how our translationbased verification method [15] is accommodated to the case of modular equivalence; and how the verification of weak/visible equivalence can be optimized as a sequence of module-level tests.