In the mathematical literature, there are several papers in which fixed point results for S-contractions defined on s (R+)-metric spaces are given: N. Gheorghiu [8], PP Zabrejko and TA Makarevich [20], VG Angelov [1], M. Frigon [7], IA Rus [15]. On the other hand, there are papers containing fixed point theorems for generalized contractions defined in more general settings. For example, we mention the case of generalized Kasahara spaces, see K. Iséki [11], S. Kasahara [12] and [13], IA Rus [17], A.-D. Filip [5]. The aim of this paper is to present a fixed point theory for S-contractions in generalized Kasahara spaces (X,→, d), where d: X× X→ s (R+) is not necessarily an s (R+)-metric.