  A comparative study of optical spectra of Type Ia supernovae (SNe Ia)
obtained near 1 week, 3 weeks, and 3 months after maximum light is presented.
Most members of the four groups that were defined on the basis of maximum light
spectra in Paper II (core normal, broad line, cool, and shallow silicon)
develop highly homogeneous postmaximum spectra, although there are interesting
exceptions. Comparisons with SYNOW synthetic spectra show that most of the
spectral features can be accounted for in a plausible way. The fits show that 3
months after maximum light, when SN Ia spectra are often said to be in the
nebular phase and to consist of forbidden emission lines, the spectra actually
remain dominated by resonance scattering features of permitted lines, primarily
those of Fe II. Even in SN 1991bg, which is said to have made a very early
transition to the nebular phase, there is no need to appeal to forbidden lines
at 3 weeks postmaximum, and at 3 months postmaximum the only clear
identification of a forbidden line is [Ca II] 7291, 7324. Recent studies of SN
Ia rates indicate that most of the SNe Ia that have ever occurred have been
"prompt" SNe Ia, produced by young (100,000,000 yr) stellar populations, while
most of the SNe Ia that occur at low redshift today are "tardy", produced by an
older (several Gyrs) population. We suggest that the shallow silicon SNe Ia
tend to be the prompt ones.
