  In this work, we study spacelike and timelike surfaces of revolution in
Minkowski space $\e_{1}^{3}$ that satisfy $aH+bK=c$, where $H$ and $K$ denote
the mean curvature and the Gauss curvature of the surface and $a$, $b$ and $c$
are constants. The classification depends on the causal character of the axis
of revolution and in all the cases, we obtain a first integral of the equation
of the generating curve of the surface.
