We investigate the band structure in GaAs quantum wells in the presence of an electric field applied along the growth direction (z) and a magnetic field perpendicular to it. The strong coupling between heavy and light holes gives rise to a nonquadratic behavior of the hole states as a function of the magnetic field. The presence of the electric field introduces new transitions by breaking the z symmetry and by coupling with the magnetic field. The Kramers degeneracy is also lifted by the external fields. The results are discussed in terms of band-to-band transitions. © 1988 The American Physical Society.