A recently reported anomaly in the time structure of signals in the KA
RMEN neutrino detector suggests the decay of a new particle x, produce
d in pi(+) --> mu(+)x with mass m(x) = 33.9 MeV. We discuss the constr
aints and difficulties in interpreting x as a neutrino. We show that a
mainly-sterile neutrino scenario is compatible with all laboratory co
nstraints, within narrow limits on the mixing parameters, although the
re are problems with astrophysical and cosmological constraints. This
scenario predicts that appreciable numbers of other x-decay events wit
h different origins and time structures should also be observable in t
he KARMEN detector. Such x-decay events should also be found in the LS
ND experiment and:may be relevant to the search for <($) over bar nu>(
mu) --> <($) over bar nu>(e) oscillations.