  The effective dynamics of the low-frequency modes is derived for the O(N)
symmetric scalar field theory in the broken symmetry phase. The effect of the
high-frequency fluctuations is taken into account at one-loop level exactly. A
new length scale is shown to govern the long-time asymptotics of the linear
response function of the Goldstone modes. The large time asymptotic decay of an
arbitrary fluctuation is determined in the linear regime. We propose a set of
local equations for the numerical solution of the effective non-linear
dynamics. The applicability of the usual gradient expansion is carefully
assessed.
