  In this paper, we consider the idea of Bertrand curves for curves lying on
surfaces in Minkowski 3-space. By considering the Darboux frame, we define
these curves as Bertrand D-curves and give the characterizations for those
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 in Minkowski 3-space, the definition and the characterizations of
Bertrand D-curves include those of Bertrand curves in some special cases.
