  Some extensions of the standard model contain additional leptons which are
vectorlike under weak isospin. A class of models is considered in which these
leptons do not appreciably mix with the known leptons. In such models, the
heavy charged lepton and the heavy neutrino are degenerate in mass, and the
degeneracy is broken by radiative corrections. The mass splitting is calculated
and found to be very weakly dependent on the lepton mass, varying from 250 to
330 MeV as the mass varies from 100 to 800 GeV. This result is {\it not}
affected significantly by inclusion in a supersymmetric model in spite of the
additional loops involving the superpartners. As a result, this fairly general
class of models has a charged lepton whose lifetime varies in the narrow range
from 0.5 to 2.0 nanoseconds, and which decays into neutrals plus a very low
energy electron or muon.
