We report on the star formation histories and extinction in the central kiloparsec region of a sample of starburst galaxies that have similar far-infrared (FIR), 10 μm, 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 and 7000 Å, and the K-band and FIR flux. A good fit requires a minimum of three 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 birthrate parameter, which is defined as the ratio of the current star formation rate to the average past rate, is found to be in the range 1-12. 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 intermediateage 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 Å break and the Ca II K line. The extinction of the old population is found to be around half 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 Hα and Hβ lines, respectively.
