In this paper, some characteristic properties of ruled surfaces which are generated by the Darboux frame of the transversal intersection timelike curve of two timelike surfaces were studied in Lorentz-Minkowski 3-Space . Moreover, the relations between the Darboux frames, the Darboux derivate formulas, the apex angles, the pitchs, the geodesic curvatures, the normal curvatures, the geodesic torsions and the dralls of the ruled surfaces were given. Then, some characterizations were investigated for the transversal intersection curves. Namely, in the case of the intersection curves were geodesic lines and asymptotic lines, some corollaries were investigated. Lastly, examples were given and the figures were drawn using Maple.
Key words. Transversal intersection spaclike curve, ruled surface, geodesic curvatures.
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