  We discuss the possibility of non-exponential tunneling ionization of atoms
irradiated by intense laser field. This effect can occur at times, which are
greater than the lifetime of a system under consideration. The mechanism for
non-exponential depletion of an initial quasi-stationary state is the cutting
of the energy spectrum of final continuous states at long times. We first
consider the known examples of cold emission of electrons from metal, tunneling
alpha-decay of atomic nuclei, spontaneous decay in two-level systems and the
single-photon atomic ionization by a weak electromagnetic field. The new
physical situation discussed is tunneling ionization of atoms by a strong
low-frequency electromagnetic field. In this case the decay obeys ~1/t
power-law dependence on the (long) interaction times.
