  The Higgs boson may decay mainly to an invisible mode characterized by
missing energy, instead of the Standard Model channels. This is a generic
feature of many models where neutrino masses arise from the spontaneous
breaking of ungauged lepton number at relatively low scales, such as
spontaneously broken R-parity models. Taking these models as framework, we
reanalyze this striking suggestion in view of the recent data on neutrino
oscillations that indicate non-zero neutrino masses. We show that, despite the
smallness of neutrino masses, the Higgs boson can decay mainly to the invisible
Goldstone boson associated to the spontaneous breaking of lepton number. This
requires a gauge singlet superfield coupling to the electroweak doublet
Higgses, as in the Next to Minimal Supersymmetric Standard Model (NMSSM)
scenario for solving the $\mu$-problem. The search for invisibly decaying Higgs
bosons should be taken into account in the planning of future accelerators,
such as the Large Hadron Collider and the Next Linear Collider.
