The inclusive B --> <X(s) nu(nu)over bar>> decay rate, on which no exp
erimental bound exists to date, can be constrained by searching for la
rge missing energy events in B decays. Carefully examining the experim
ental and theoretical aspects of such an analysis, we argue that the p
ublished ALEPH limit on BR(B --> tau<(nu)over bar>) implies, conservat
ively, the bound BR(B --> <X(s) nu(nu)over bar>) < 3.9 x 10(-4), which
is less than one order of magnitude above the standard model predicti
on. The LEP collaborations could significantly improve this bound by a
dedicated experimental analysis. We study the constraints this new Li
mit imposes on various extensions of the standard model. We derive new
bounds on the couplings of third generation fermions in models with l
eptoquarks, and in supersymmetric models without R-parity. We also con
strain models where new gauge bosons are coupled dominantly to the thi
rd generation, such as TopColor models and models based on horizontal
gauge symmetries, For models which predict an enhanced effective bsZ v
ertex, the constraint from B --> <X(s) nu(nu)over bar> is competitive
with the limits from inclusive and exclusive B --> X(s)l(+)l(-) decays
.