  We study the central (inner few hundred parsecs) stellar populations of four
starburst galaxies (NGC34, NGC1614, NGC3310 and NGC7714) in the near-infrared
(NIR), from 0.8 to 2.4microns, by fitting combinations of stellar population
models of various ages and metallicities. The NIR spectra of these galaxies
feature many absorption lines. For the first time, we fit simultaneously as
much as 15 absorption features in the NIR. The observed spectra are best
explained by stellar populations containing a sizable amount (20 to 56 % by
mass) of ~1Gyr old stellar population with Thermally Pulsing-Asymptotic Giant
Branch stars. We found that the metallicity of the stars which dominates the
light is solar. Metallicities substantially different from solar give a worse
fit. Though the ages and metallicities we estimate using the NIR spectroscopy
are in agreement with values from the literature based on the UV/optical, we
find older ages and a larger age spread. This may be due to the fact that the
optical is mostly sensitive to the last episode of star formation, while the
NIR better maintains the record of previous stellar generations. Another
interesting result is that the reddening estimated from the whole NIR spectrum
is considerably lower than that based on emission lines. Finally, we find a
good agreement of the free emission line spectrum with photoionization models,
using as input spectral energy distribution the synthetic composite template we
derived as best-fit.
