(Abridged) As part of an ongoing effort to study the stellar nuclei of very late-type, bulge-less spirals, we present results from a high-resolution spectroscopic survey of nine such nuclear star clusters, undertaken with VLT/UVES. We fit the spectra with population synthesis models and measure Lick-type indices to determine mean luminosity-weighted ages, which range from 4.1*10^7 to 1.1*10^10 years and are insensitive to assumed metallicity or internal extinction. The average metallicity of nuclear clusters in late-type spirals is slightly sub-solar (<Z> = 0.015) but shows significant scatter. The fits also show that the nuclear cluster spectra are best described by a mix of several generations of stars. This is supported by the fact that only models with composite stellar populations yield mass-to-light ratios that match those obtained from dynamical measurements. The last star formation episode was on average 34 Myr ago, while all clusters experienced some star formation in the last 100 Myr. We thus conclude that the nuclear clusters undergo repeated episodes of star formation. The robustness with respect to possible contamination from the underlying galaxy disk is demonstrated by comparison to spectra obtained with HST/STIS. Combining these results with those from Walcher et al. (2005), we have thus shown that the stellar nuclei of these bulge-less galaxies are massive and dense star clusters that form stars recurrently until the present day. This unique set of properties is likely due to the central location of these clusters in their host galaxies.
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