  In this paper we consider the idea of Bertrand curves for curves lying on
surfaces and by considering the Darboux frames of them we define these curves
as Bertrand D-curves and give the characterizations for these curves. We also
find the relations between the geodesic curvatures, the normal curvatures and
the geodesic torsions of these associated curves. Furthermore, we show that the
definition and the characterizations of Bertrand D-curves include those of
Bertrand curves in some special cases.
