  We report on the star formation histories and extinction in the central kpc
region of a sample of starburst galaxies that have similar far infrared (FIR),
10 micron and K-band luminosities as those of the archetype starburst M82. Our
study is based on new optical spectra and previously published K-band
photometric data, both sampling the same area around the nucleus. Model
starburst spectra were synthesized as a combination of stellar populations of
distinct ages formed over the Hubble time, and were fitted to the observed
optical spectra and K-band flux. The model is able to reproduce simultaneously
the equivalent widths of emission and absorption lines, the continuum fluxes
between 3500-7000 Ang, the K-band and the FIR flux. We require a minimum of 3
populations -- (1) a young population of age < 8 Myr, with its corresponding
nebular emission, (2) an intermediate-age population (age < 500 Myr), and (3)
an old population that forms part of the underlying disk or/and bulge
population. The contribution of the old population to the K-band luminosity
depends on the birthrate parameter and remains above 60% in the majority of the
sample galaxies. Even in the blue band, the intermediate age and old
populations contribute more than 40% of the total flux in all the cases. A
relatively high contribution from the old stars to the K-band nuclear flux is
also apparent from the strength of the 4000 Ang break and the CaII K line. The
extinction of the old population is found to be around half of that of the
young population. The contribution to the continuum from the relatively old
stars has the effect of diluting the emission equivalent widths below the
values expected for young bursts. The mean dilution factors are found to be 5
and 3 for the Halpha and Hbeta lines respectively.
