  Hamilton-Jacobi equation for Brans-Dicke theory is solved by using a
long-wavelength approximation. We examine the non-linear evolution of the
inhomogeneities in the dust fluid case and the cosmological constant case. In
the case of dust fluid, it turns out that the inhomogeneities of space-time
grow. In the case of cosmological constant, the inhomogeneities decay, which is
consistent with the cosmic no hair conjecture. The inhomogeneities of the
density perturbation and the gravitational constant behave similarly with that
of space-time.
