We present the results of a study of the temporal behavior of several diagnostic lines formed in the region of the accretion-disk/star interaction in the three magnetic Herbig Ae stars HD 101412, HD 104237, and HD 190073. More than 100 spectra acquired with the ISAAC, X-shooter, and CRIRES spectrographs installed at the 8-m VLT telescope (ESO, Chile), as well as at other observatories (OHP, Crimean AO) were analyzed. The spectroscopic data were obtained in the He I λ10 830, Paγ, and He I λ5876 lines. We found that the temporal behavior of the diagnostic lines in the spectra of all program stars can be widely explained by a rotational modulation of the line profiles, generated by a local accretion flow. This result is in good agreement with the predictions of the magnetospheric accretion model. For the first time, the rotation period of HD 104237 (Prot = 5.37±0.03 days) as well as the inclination angle (i = 21°±4°) were determined. Additional analysis of the HARPSpol spectra of HD 104237 and HD 190073, taken f