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In this work, we study spacelike and timelike surfaces of revolution inMinkowski space $\e_{1}^{3}$ that satisfy $aH+bK=c$, where $H$ and $K$ denotethe 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 axisof revolution and in all the cases, we obtain a first integral of the equationof the generating curve of the surface.

Non-degenerate surfaces of revolution in Minkowski space that satisfy the relation $aH+bK=c$