In this paper, we present the results for the post-AGB phases of stellar evolutionary sequences, complete from the main-sequence phase, through the AGB phase, and on into the planetary nebula and white dwarf regimes. Mass loss has been included using an empirical formalism derived from observed mass-loss rates of planetary nebula nuclei available in the literature and from radiation-pressure-driven stellar wind theory. Models are calculated for initial masses 0.89, 0.95, 1.0, 1.5, 2.0, 2.5, 3.5, and 5.0M_{sun}_, and metallicities 0.016, 0.008, 0.004, and 0.001. These abundance and mass values were chosen to allow comparison with Galactic, and Magellanic Cloud planetary nebulae and their nuclei. The post-AGB evolutionary sequences fall into two distinct groups depending on when the planetary nebula nuclei leave the AGB: one group where helium-shell burning is dominant, and the other group where hydrogen-shell burning is dominant. Of the 27 computed sequences: 17 are hydrogen-burners, and 10 are helium-burners. In only five cases was any effort made to control the phase of departure from the AGB. Lower mass models are more likely to leave the AGB burning helium, as the preceding AGB evolution has a mass-loss rate which is greatest immediately prior to a helium-shell flash. The calculations are compared with the large observational database that has developed over recent years for the Large Magellanic Cloud. These calculations will be useful for determining the planetary nebula luminosity function, and for the study of the ultraviolet excess observed in elliptical galaxies. Addresses: Vassiliadis E. Mount Stromlo and Siding Spring Observatories, Institute of Advanced Studies, The Australian National Observatory, Private Bag, Weston Creek P.O., A.C.T. 2611, Australia Wood P.R. Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218