This paper proposes a mapping between two product quality and software processes models used in the industry, the CERTICS Brazilian national model and the CMMI-DEV international model. The focus of this mapping is in the Technological Development Competence Area of CERTICS, which directs the response to the key question on whether "the software is the result of technological development in the country". The results of mapping are presented step by step, as well as the mapping review, which had the cooperation of one expert in CERTICS and CMMI-DEV models. Thus, this paper aims to correlate the structures of the two models in order to facilitate and reduce the implementation time and costs, and to stimulate the execution of multi-model implementations in software development enterprises.