The requirements for conformance of a process model to the international standard for process assessment, ISO/IEC 15504, cover a broad range. The most significant of these is the need to establish a complete and unambiguous mapping between the Process Assessment Model and the relevant Process Reference Model and theMeasurement Framework described in the Standard. This is required to support the development of a mechanism for translating the outputs from an assessment using the Process Assessment Model into the standard process profiles defined in ISO/IEC 15504. This article reports the results of an analysis of the relationship between CMMI, as a 'candidate conformant Process Assessment Model', relative to the Measurement Framework defined in ISO/IEC 15504-2, and the Process Reference Model described in ISO/IEC 12207 Amd 1/2. It is shown that, while in general terms a complete mapping can be established, there are specific areas where coverage is weak. Use of CMMI as a Process Assessment Model in ISO/IEC 15504 Conformant assessments will need to take account of these issues.