We present spectral analysis of ASCA data of 17 elliptical and three lenticular galaxies most of which have high L-x/L-B. Single-temperature models (MEKAL and Raymond-Smith) give unacceptable fits (chi(red)(2) > 1.5) in most cases and, in agreement with previous studies, give very subsolar abundances, (Z) = 0.19 +/- 0.12 Z. (MEKAL). The spectra for approximately half the sample are fitted better by a cooling-flow model, which in three cases gives a substantially better fit. The abundances derived from the cooling-how model are also significantly larger, (Z) = 0.6 +/- 0.5 Z.. We empirically tested the reliability of the plasma codes in the Fe L region and found no evidence for serious problems with the determined temperatures and abundances. Two-temperature models give substantially better fits that are formally acceptable (chi(red)(2) similar to 10) in all but a few cases. The highest signal-to-noise ratio galaxies (which also have highest L-x/L-B) have fitted temperatures < 2 keV for both components consistent with each being distinct phases of hot gas. The lowest signal-to-noise ratio galaxies (which also have lowest L-x/L-B) generally have a hot component with temperature, T-H greater than or similar to 5 keV, which is consistent with emission from discrete sources. (We discuss the origin of these two components from analysis of L-x-L-B and L-x/L-B.) The abundances of these two-temperature models are approximately solar, (Z) = 0.9 +/- 0.7 Z. (MEKAL), consistent with a recent multiphase model for the evolution of hot gas in ellipticals. Finally, for several galaxies we find evidence for absorption in excess of the Galactic value and discuss its implications.