The evaluation of the "maturity" of organizations involved in systems and software engineering has become an important issue. It is generally agreed that a rating of "maturity" should be able to be derived from the set of process capability ratings (the "process profile") obtained from a formal process assessment. However, there are issues in the determination of "maturity" using existing approaches; among the major concerns are the scope of the organizational unit for which a valid determination of maturity can be made; the minimum scope of the process model that can be used for such an assessment; and the degree of rigor required in the assessment. This paper clarifies a number of these issues, and describes the work in progress to develop a new part of the International Standard for Process Assessment that will cover the topic of assessment of organizational maturity.