Relativistic corrections to the electronic energies are computed for the EF, GK, and H (H) over bar (1)Sigma(g) states of the hydrogen molecule in a wide range of internuclear distances. Term values for the J=0 levels are given for the EF state and for the outer well of the H (H) over bar state. A comparison with experiment shows that the adiabatic, relativistic theoretical H (H) over bar energies are too low by about 1 cm(-1).