It follows from the analysis of the precision numerical calculations of the energy spectrum of a hydrogen atom in a static magnetic field that the Zeldovich effect (rearrangement of the atomic spectrum) in the spectrum of atomic levels is observed at superstrong magnetic fields B ≥ 5 × 10[sup 11] G. Magnetic fields of such strengths are reached in neutron stars and magnetic white dwarfs. We established a lower bound B[sub min] for the fields required for this effect to occur.