  The resonant spectra of hydrogen and anti-hydrogen atoms in the presence of
an external electric field are compared theoretically. It is shown that
nonresonant corrections to the transition frequency contain terms linear in the
electric field. The existence of these terms does not violate space and time
parity and leads to a difference in the resonant spectroscopic measurements for
hydrogen and anti-hydrogen atoms in an external electric field. The one-photon
1s-2p and the two-photon 1s-2s resonances are investigated.
