We consider transitions between neutrinos and antineutrinos in laborat
ory experiments in five scenarios. These include the case in which the
helicity flips, producing an antineutrino with normal weak interactio
ns, and helicity preserving oscillations into an SU(2) singlet state w
hich only interacts by mixing or new interactions. The ratio of mu(+)
and mu(-) events for a high energy nu(mu) beam from pion decay rescatt
ered from a nucleon target and the ratio between e(+) and e(-) events
for a rescattered low energy v(e) beam are calculated in each case. Th
e upper limit on the ratio is about 10(-6)-10(-10) for a high energy n
u(mu) beam and 10(-6)-10(-14) for a low energy nu(e) beam, too small t
o observe in present experiments. [S0556-2821(98)05615-X].