  To understand the nuclear stellar populations and star formation histories of
the nuclei of spiral galaxies, we have obtained K-band nuclear spectra for 41
galaxies and H-band spectra for 20 galaxies in the ISO Atlas of Bright Spiral
Galaxies. In the vast majority of the subsample (80%), the near-infrared
spectra suggest that evolved red stars completely dominate the nuclear stellar
populations and that hot young stars are virtually non-existent. The signatures
of recent star formation activity are only found in 20% of the subsample, even
though older red stars still dominate the stellar populations in these
galaxies. Given the dominance of evolved stars in most galaxy nuclei and the
nature of the emission lines in the galaxies where they were detected, we
suggest that nuclear star formation proceeds in the form of instantaneous
bursts. The stars produced by these bursts comprise only ~2% of the total
nuclear stellar mass in these galaxies, but we demonstrate how the nuclear
stellar populations of normal spiral galaxies can be built up through a series
of these bursts. The bursts were detected only in Sbc galaxies and later, and
both bars and interactions appeared to be sufficient but not necessary triggers
for the nuclear star formation activity. The vast majority of galaxies with
nuclear star formation were classified as HII galaxies. With one exception,
LINERs and transition objects were dominated by older red stars, which
suggested that star formation was not responsible for generating these
galaxies' optical line emission.
