  We have shown that the dynamics of the scalar field $\phi (x)= ``G^{-1}(x)"$
in Brans-Dicke theories of gravity makes the surface area of the black hole
horizon {\it oscillatory} during its dynamical evolution. It explicitly
explains why the area theorem does not hold in Brans-Dicke theory. However, we
show that there exists a certain non-decreasing quantity defined on the event
horizon which is proportional to the black hole entropy for the case of
stationary solutions in Brans-Dicke theory. Some numerical simulations have
been demonstrated for Oppenheimer-Snyder collapse in Brans-Dicke theory.
