We analyse the stellar absorption features in high signal-to-noise ratio (S/N) near-infrared (NIR) spectra of the nuclear region of 12 nearby galaxies, mostly spirals. The features detected in some or all of the galaxies in this sample are the TiO (0.843 and 0.886 μm), VO (1.048 μm), CN (1.1 and 1.4 μm), H2O (1.4 and 1.9 μm) and CO (1.6 and 2.3 μm) bands. The C2 (1.17 and 1.76 μm) bands are generally weak or absent, although C2 (1.76 μm) may be weakly present in the mean galaxy spectrum. A deep feature near 0.93 μm, likely caused by CN, TiO and/or ZrO, is also detected in all objects. Fitting a combination of stellar spectra to the mean spectrum shows that the absorption features are produced by evolved stars: cool giants and supergiant stars in the early- or thermally pulsing asymptotic giant branch (E-AGB or TP-AGB) phases. The high luminosity of TP-AGB stars, and the appearance of VO and ZrO features in the data, suggest that TP-AGB stars dominate these spectral features. However, a contribution from other evolved stars is also likely. Comparison with evolutionary population synthesis models shows that models based on empirical libraries that predict relatively strong NIR features provide a more accurate description of the data. However, none of the models tested accurately reproduces all of the features observed in the spectra. To do so, the models will need to not only improve the treatment of TP-AGB stars, but also include good quality spectra of red giant and E-AGB stars. The uninterrupted wavelength coverage, high S/N and quantity of features we present here will provide a benchmark for the next generation of models aiming to explain and predict the NIR properties of galaxies.