Classical mechanics has been applied in the theoretical study of the ionization of hydrogen atoms by static electric and circularly polarized electromagnetic fields. In both cases it was assumed that the ionizing field was adiabatically switched on. In the case of circular fields the calculations were performed for the initial energies E 0 = −1/2n 2 0 and frequencies of the field ω for which ωn 3 0 0.44. For such initial conditions almost all trajectories that lead to ionization are regular. The results of adiabatic theory and numerical simulations are compared with recent experiments.