The ionospheric effects of the great geomagnetic storms of 30--31 October and 20--21 November 2003 observed over Alma-Ata (43.25¿N, 76.92¿E) were studied experimentally using ground-based ionosondes. The observations showed a number of unusual (for the Alma-Ata location) ionospheric phenomena during the active phase of the geomagnetic storms. It is a very high F2 layer (h'F ≥ 490 km), an anomalous formation of the E, E2, and F1 layers at nighttime, and the appearance of auroral-type sporadic E layers. Processes of interaction of energetic neutrals with the upper atmosphere modeled by Bauske et al. (1997) for magnetically disturbed conditions seem to explain the phenomena of ionization of F1 and E regions at night.