  We consider Brans-Dicke (BD) scalar tensor theory in the conformally
transformed Einstein frame. In this frame BD theory behaves like an interacting
quintessence model. We find the necessary conditions on the form of the
potential $V(\varphi)$ in order to have thawing behavior. Finally, by setting
the BD coupling constant $\omega=0$, the metric $f(R)$ gravity has been
considered in the Einstein frame. Assuming the existence of thawing solution,
some necessary conditions for $f(R)$ gravity models have been derived.
