  Given a constant vector field $Z$ in Minkowski space, a timelike surface is
said to have a canonical null direction with respect to $Z$ if the projection
of $Z$ on the tangent space of the surface gives a lightlike vector field. In
this paper we describe these surfaces in the ruled case. For example when the
Minkowski space has three dimensions then a surface with a canonical null
direction is minimal and flat. On the other hand, we describe several
properties in the non ruled case and we partially describe these surfaces in
four-dimensional Minkowski space. We give different ways for building these
surfaces in four-dimensional Minkowski space and we finally use the Gauss map
for describe another properties of these surfaces.
