  We study second-order cosmological perturbations in scalar-tensor models of
dark energy that satisfy local gravity constraints, including f(R) gravity. We
derive equations for matter fluctuations under a sub-horizon approximation and
clarify conditions under which first-order perturbations in the scalar field
can be neglected relative to second-order matter and velocity perturbations. We
also compute the skewness of the matter density distribution and find that the
difference from the LCDM model is only less than a few percent even if the
growth rate of first-order perturbations is significantly different from that
in the LCDM model. This shows that the skewness provides a model-independent
test for the picture of gravitational instability from Gaussian initial
perturbations including scalar-tensor modified gravity models.
