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We consider the research and development(R&D) investment com-petition of duopolistic firms in completely complementarty technolo-gies. By ”completely complementary technologies, ” we mean that no firm can produce the goods without both of the technologies. We derive the investments competiton equilibria in R&D of the two com-pletely complementary technologies with and without a cross-licensing system. By comparing R&D investment levels in the two equilibria, we show that the cross-licensing system discourages the R&D invest-ments when the duopolistic firms produce goods by using the two completely complementary technologies. Key Words: completely complementary technologies, cross-licensing sys