  The triviality and vacuum stability bounds on the Higgs-boson mass ($\mh$)
were revisited in presence of weakly-coupled new interactions parameterized in
a model-independent way by effective operators of dimension 6. The constraints
from precision tests of the Standard Model were taken into account. It was
shown that for the scale of new physics in the region $\Lambda \simeq 2 \div 50
\tev$ the Standard Model triviality upper bound remains unmodified whereas it
is natural to expect that the lower bound derived from the requirement of
vacuum stability is substantially modified depending on the scale $\La$ and
strength of coefficients of effective operators. A natural generalization of
the standard triviality condition leads also to a substantial reduction of the
allowed region in the ($\Lambda,\mh$) space.
