  It is shown that in a large class of E(6) models, either an e+e- collider
operating at $\rs \geq 1.5$ TeV must find a signal for the production of exotic
leptons, or a collider operating at $\rs \geq 300$ GeV must find at least one
light neutral Higgs boson with a large invisible branching ratio. The region of
parameter space where neither of these signals is visible can be excluded
because here the lightest neutral exotic lepton, which is absolutely stable,
would overclose the Universe.
