The problems concerning the development of high f-number spectrographs with high spectral and spatial resolution using holographic reflecting gratings, for the study of processes of harmonic generation in laser plasmas are considered. The concave holographic gratings and spectrograph schemes used in the “Delfin-1” installation are described. The anomalous generation of ω0 and 2ω0 harmonics from the subcritical density plasma region has been observed experimentally. Possible interpretations of the observed effect are given.