  A possibility of the two-photon excitation of an isomeric state in a nucleus
of thorium-229 has been discussed. The fluorescence intensity of the excitation
is demonstrated to be identical for the irradiation of nuclei with either
monochromatic light or polychromatic radiation consisting of a sequence of
short light pulses of the same intensity. The two-photon excitation of Th^{3+}
ion in an electromagnetic trap with a focused laser beam with a wavelength of
about 320 nm and power of 100 mW can lead to the absorption saturation, at
which the fluorescence emission with the frequency of the transition in a
nucleus is maximal. In crystals doped with Th^{4+} to a concentration of about
10^{18} cm^{-3} and irradiated with a laser radiation 10 W in power, the
emission of several photons per second with a wavelength of about 160 nm
becomes possible.
