We study instability of the scalar field oscillating around a minimum of inflaton potential

in the Friedmann-Robertson-Walker universe. It is shown that the evolution of the $k$-modes

of the scalar field perturbations is governed by the Hill equation involving the field energy

density as a parameter that changes slowly as the Universe expands. The general perturbative

approach to the Hill equation with a slowly varying parameter is developed. As an application

we consider slow passage through the resonance in the Lame equation describing the scalar

field modes in the case of $\varphi^2-\varphi^4$ potential. The asymptotic solutions obtained

by the perturbative approach are compared with the results of the direct numerical integration.

The nonlinear stage of instability and formation of the oscillating field lumps are briefly discussed.