Field-effect transistors (FETs) with channels of two-dimensional transition metal dichalcogenides (2D TMDs) are expected to extend Moore's law by extreme scaling of contacted gate pitch (CGP) post silicon-sheet-based complementary FET (CFET) devices. The ultrathin body and fully passivated surface of 2D materials result in superior electrostatic control and improved short channel behavior [1]. Challenges such as high contact resistance or lack of doping technology are on the way of 2D-FETs reaching the required performance for high-performance logic applications [2,3]. Additionally, in order to integrate 2D TMDs in ultra-scaled CMOS devices, developing a patterning scheme via the state-of-the-art extreme ultraviolet (EUV) lithography is essential [4]. In this paper we demonstrate our first results on studying the compatibility and interaction of semiconducting 2D TMDs with EUV environment using a set of characterization techniques that are fit to detect qualitative defects and morphological changes in these atomically thin layers. Our study is focused on semiconducting TMDs that are currently the most promising candidates for transistor channels: MoS2 (NMOS) and WSe2 (PMOS). We report the interaction of EUV photons and photo-electrons with blanket films of MoS2 and WSe2 for different EUV doses in vacuum environment. Based on the current findings we propose design of experiments aiming at developing controllable and tunable modification and patterning of 2D TMDs with the EUV energy and resolution for advanced device nodes.