Advanced meanline turbomachinery performance models are presented based on an extensive database for centrifugal and mixed-flow compressors and pumps. The methodology of processing the data is briefly discussed here, and in more depth in a companion paper. In this investigation, the detailed steps of building the highly non-linear, multi-variable, coupled models are presented. This modeling includes the impeller, a vaneless diffuser, and/or a volute. In future papers, diverse classes of diffusers, guide vanes, and return channels will be added as well. Using genetic expression programming, models of very high order are developed. These models are then tested against neural network models that are built using the same database. Several different classes of performance models are built to meet global modeling requirements, specific discipline domain requirements, and to meet specific designers’ requirements. This paper is one in a set of four papers. Papers No. 1 and 4 were presented at the ASME/IGTI Conference in Reno, Nevada, on June 6–9, 2005, and the remaining two (Papers No. 2 and No. 3) are being presented at the 2005 ASME International Mechanical Engineering Congress on November 5–11, 2005, in Orlando, Florida.Copyright © 2005 by Concepts ETI, Inc.