In this paper, timelike and spacelike tubularWeingarten surfaces inMinkowski 3-space which satisfies nontrivial relation between elements of the set {K, KII, H, HII}, where (K, H) and (KII , HII) are the Gaussian and mean curvatures of the first and second fundamental forms, respectively are studied. An additional results for tubular L/W-surfaces are obtained. Moreover, for some special cases new examples are constructed and plotted. [ABSTRACT FROM AUTHOR]