  Assuming three flavour neutrino mixing takes place in vacuum, we investigate
the possibility that the solar nu_e take part in MSW transitions in the Sun due
to Delta m^2_{31} from 10^{-7} eV^2 to 10^{-4} eV^2, followed by long wave
length vacuum oscillations on the way to the Earth, triggered by Delta m^2_{21}
(or Delta m^2_{32}) from 10^{-12} eV^2 to 10^{-10} eV^2, Delta m^2_{31} and
Delta m^2_{21} (Delta m^2_{32}) being the corresponding neutrino mass squared
differences. The solar nu_e survival probability is shown to be described in
this case by a simple analytic expression. Depending on whether the vacuum
oscillations are due to Delta m^2_{21} or Delta m^2_{32} there are two very
different types of interplay between the MSW transitions and the vacuum
oscillations of the solar nu_e. Performing an analysis of the most recently
published solar neutrino data we have found several qualitatively new solutions
of the solar neutrino problem of the hybrid MSW transitions + vacuum
oscillations type. The solutions differ in the way the pp, 7Be and 8B neutrino
fluxes are affected by the transitions in the Sun and the oscillations in
vacuum. The specific features of the new solutions are discussed.
