  The evolution of linear cosmological perturbations in modified theories of
gravity is investigated assuming the Palatini formalism. It has been discussed
about the stability problem in this model based on the equivalence between f(R)
gravity and the scalar tensor theory. However, we study this problem in the
physical frame where the matter is minimally coupled. In general, the stability
of the superhorizon metric evolution depends on models. We show that the
deviation from the superhorizon metric evolution is null for a specific choice
for the nonlinear Einstein-Hilbert action, $f(\hat{R}) \sim \hat{R}^{n}$, where
$n \neq 0,2,3$. Thus the stability of metric fluctuation is guaranteed in these
models. We also study the matter density fluctuation in the general gauge and
show the differential equations in super and sub-horizon scales.
