We show that, for Majorana neutrinos propagating in a constant magnetic fie
ld, the flavor survival probabilities for left-handed neutrinos are the sam
e as for right-handed neutrinos, i.e., P-M(nu(alpha L) --> nu(alpha L)) = P
-M (nu(alpha R) --> nu(alpha R)), where alpha = e, mu, tau, whereas in the
Dirac case the corresponding probabilities P-D(nu(alpha L) --> nu(alpha L))
and P-D(<(nu)over bar>R --> <(nu)over bar>(alpha R)) are in general differ
ent. This might lead to a novel way to search for the nature of neutrinos.
We also discuss how this relation for Majorana neutrinos gets modified when
the magnetic field is not constant. However, if matter effects become impo
rtant, the relation does not hold anymore.