  In this work, we investigate the preheating mechanism after inflation in
general scalar-tensor theories of gravity. In the present scenario, we consider
two-field scenario and then derive the potential of exponential and hyperbolic
tangent forms. We study the evolution of the background system when the back
reaction on the background field is neglected. We examine the particle
production due to parametric resonances in both models. We find that in
Minkowski space the stage of parametric resonances can be described by the
Mathieu equation. Finally, we demonstrate that parametric resonances in our
models are sufficiently broad possible for the exponential growth of the number
of particles.
