Abstract
Let M and M* be two timelike surfaces in Minkowski 3-space Double-struck capital R-1(3). If there exists a spacelike (timelike) Darboux line congruence between each point of M and M*, then the surfaces are timelike Weingarten surfaces. It turns out their Tschebyscheff angles are solutions of the Sinh-Gordon equation, and the surfaces are related to each other by Backlund's transformation. Finally, a method to construct new timelike Weingarten surface has been found.