This report presents the details of the governing equations, physical parameterizations, and numerical algorithms defining the version of the NCAR Community Climate Model designated CCM3. The material provides an overview of the major model components, and the way in which they interact as the numerical integration proceeds. Details on the coding implementation, along with in-depth information on running the CCM3 code, are given in a separate technical report entitled "User's Guide to NCAR CCM3" (Acker et al., 1996). As before, it is our objective that this model provide NCAR and the university research community with a reliable, well documented atmospheric general circulation model. This version of the CCM incorporates significant improvements to the physics package, new capabilities such as the incorporation of a slab ocean component, and a number of enhancements to the implementation (e.g., the ability to integrate the model on parallel distributed-memory computational platforms). We believe that collectively these improvements provide the research community with a significantly improved atmospheric modeling capability.