The succession of the Capability Maturity Model for Software (SW-CMM) and the System Engineering Capability Maturity Model (EIA/IS 731) by the Capability Maturity Model-Integrated (CMMI) will expose many organizations that currently use either the SW-CMM or the SE-CMM to the challenge of an effective and efficient transition from the old models to the new one. This paper advises on how this transition can be accomplished. This paper was updated in January 2003 with TR 15504 / SPICE to CMMI mapping in an appendix.