  We study Pontecorvo neutrino-antineutrino oscillations both in vacuum and in
matter within a field theoretic approach, showing that this phenomenon can
occur only if neutrinos have a Dirac-Majorana mass term. We find that matter
effects suppress these oscillations and cannot explain the solar neutrino
problem. On the contrary, a vacuum neutrino-antineutrino oscillations solution
to this problem exists. We analyze this solution and available data from
laboratory experiments giving stringent limits on $\nu_e$ and $\nu_{\mu}$
Majorana masses.
