  We give examples showing that two well-known versions of the S-matrix theory,
which describes a nonresonant multiphoton ionization of atoms and ions in
intense laser fields, lead to qualitatively different results. The latter refer
not only to total ionization rates, but also to energy distributions of
photoelectrons, for instance in a polarization plane of the laser field. It
should be possible to make an experiment testing predictions of both theories
in the near future.
