  We consider Brans-Dicke type nonminimally coupled scalar field as a candidate
for dark energy. In the conformally transformed Einstein's frame, our model is
similar to {\it coupled quintessence} model. In such models, we consider
potentials for the scalar field which satisfy the slow-roll conditions:
$[(1/V)(dV/d\phi)]^2 << 1$ and $(1/V)(d^2V/d\phi^2) << 1$. For such potentials,
we show that the equation of state for the scalar field can be described by a
universal behaviour, provided the scalar field rolls only in the flat part of
the potentials where the slow-roll conditions are satisfied. Our work
generalizes the previous work by Scherrer and Sen \cite{scherrer} for minimally
coupled scalar field case. We have also studied the observational constraints
on the model parameters considering the Supernova and BAO observational data.
