Sitzungsber. Abt. II (2004) 213: 23–32 Transversal Surfaces of Ruled Surfaces in the Pseudo-Galilean Space By Z ˇ eljka Milin S ˇ ipus ˇ and Blaz ˇenka Divjak (Vorgelegt in der Sitzung der math.-nat. Klasse am 22. Ja ¨nner 2004 durch das w. M. Ludwig Reich) Abstract In this paper we describe the transversal surfaces of ruled surfaces in the pseudo- Galilean space G 1 3 . There are three types of transversal surfaces. The obtained results can be easily transferred to the Galilean space G 3 . Mathematics Subject Classification (2000): 53A35. Key words and phrases: Pseudo-Galilean space, Galilean space, transversal surface, ruled surface. 1. Introduction In the three-dimensional Euclidean space E 3 the notion of -transversal surfaces was defined in the works of G. PIRONDINI and later in the works of K. GOROWARA. H. SACHS [6] studied -transversal surfaces, as well as - and -transversal surfaces, by means of natural invariants [4] of ruled surfaces. The same objects in simply isotropic space I 1 3 were studied by A. T AOUKTSOGLOU in [7] for the ruled surfaces of the most general type. The pseudo-Galilean space G 1 3 is the three-dimensional real affine space with the absolute figure f!; f ; I g, where ! is a fixed plane, f a line in ! and I a hyperbolic involution of the points of f . The absolute figure in the Galilean space G 3 has an elliptic involution instead of the