We present evolutionary stellar population synthesis models to predict the spectrum of a single-metallicity stellar population, with a spectral sampling of 0.3 Å in five spectral regions between 3700 and 5000 Å. The models, which are optimized for galaxies with active star formation, synthesize the profiles of the hydrogen Balmer series (Hβ, Hγ, Hδ, H8, H9, H10, H11, H12 and H13) and the neutral helium absorption lines (HeI λ4922, HeI λ4471, HeI λ4388, HeI λ4144, HeI λ4121, HeI λ4026, HeI λ4009 and HeI λ3819) for a burst with an age ranging from 10 6 to 10 9 yr, and different assumptions about the stellar initial mass function (IMF). Continuous star formation models lasting for 1Gyr are also presented. The input stellar library includes NLTE absorption profiles for stars hotter than 25000 K and LTE profiles for lower temperatures.The temperature and gravity coverage is 4000 K ≤T ef f ≤50000 K and 0.0≤log g≤5.0, respectively. The metallicity is solar.It is found that the Balmer and HeI line profiles are sensitive to the age, except during the first 4 Myr of the evolution, when the equivalent widths of these lines are constant. At these early stages of the evolution, the profiles of the lines are also sensitive to the IMF. However, strong H Balmer and HeI lines are predicted even when the low mass cut-off of the IMF is as high as 10 M⊙.The equivalent widths of the Balmer lines range from 2 to 16 Å and the HeI lines from 0.2 to 1.2 Å. During the nebular phase (cluster younger than about 10 Myr), Hβ ranges from 2 to 5 Å and HeI λ4471 between 0.5 and 1.2 Å. The strength of the lines is maximum when the cluster is a few hundred (for the Balmer lines) and a few ten (for the HeI lines) Myr old. In the continuous star formation scenario, the strength of the Balmer and HeI lines increases monotonically with time until 500 Myr and 100 Myr, respectively. However, the The models can be used to date starburst and post-starburst galaxies until 1 Gyr. They have been tested on data for clusters in the LMC, the super-star cluster B in the starburst galaxy NGC 1569, the nucleus of the dwarf elliptical NGC 205 and a luminous "E+A" galaxy.
