We present a comprehensive nonequilibrium ionization (NEI) analysis of X-ray spectral data from the Einstein Observatory and EXOSAT for the supernova remnant G292.0+1.8. The spectra are well described by a single-temperature, single-timescale NEI model with kT = 1.64(sub -0.19)(sup +0.29) keV and n(sub e)t = (5.55(sub -1.12)(sup +1.2) x 10(exp 10)s/cu cm, which establishes that this remnant is indeed young and in the ionizing phase of evolution of its X-ray spectrum. We determine the abundances of the elements O, Ne, Mg, Si, S, Ar, and Fe and examine their variation over the allowed range of column density, kT, and n(sub e)t. Numerical calculations of the nucleosynthesis expected for a 25 solar mass progenitor agree best with the fitted abundances; in fact the minimum rms percent difference between this model and the derived abundances is only 15%. From the fitted emission measure and a simple geometric model of the remnant we estimate the mass of X-ray-emitting plasma to be 9.3(sub -6.2)(sup +1.19) solar mass, for an assumed distance of 4.8 +/- 1.6 kpc. Additional errors on this mass estimate, from clumping of the ejecta, for example, may be substantial. No evidence was found for a difference in the thermodynamic state of the plasma as a function of elemental composition based on analysis of the individual ionization timescales of the various species. In this sense then, G292.0+1.8 resembles the remnant Cas A (another product of a massive star supernova), while it is different from the remnants of SN 1572 (Tycho) and SN 1006, both of which are believed to be from Type Ia supernovae.