  A countable set of asymptotic space -- localized solutions is constructed by
the complex germ method in the adiabatic approximation for 3D Hartree type
equations with a quadratic potential. The asymptotic parameter is 1/T, where
$T\gg1$ is the adiabatic evolution time.
  A generalization of the Berry phase of the linear Schr\"odinger equation is
formulated for the Hartree type equation. For the solutions constructed, the
Berry phases are found in explicit form.
