Atomic layer deposition (ALD) is an enabling technology for the fabrication of many nanoscale semiconductor devices. This study focuses on ALD of ZnO on the two-dimensional (2D) materials MoS2 and WSe2. Mechanically exfoliated flakes and coalesced films of MoS2 and WSe2 acted as substrates for ALD and plasma-enhanced ALD (PEALD) of ZnO at 125 degrees C, and were investigated by atomic force microscopy, Raman spectroscopy, and X-ray photoelectron spectroscopy. The MoS2 and WSe2 surfaces resisted nucleation during thermal ALD everywhere except defects, allowing for selective growth of ZnO on the surrounding SiO2 substrate for over 500 cycles. UVO3 pre-treatment showed different results for MoS2 and WSe2. On MoS2, UV-O-3 pre-treatment was effective in inducing nucleation; ZnO was deposited on different areas of the flake with different thicknesses, and coalesced films formed, unlike ZnO deposited during thermal ALD without pretreatment. On WSe2, ZnO nucleated only on certain more reactive areas of the surface that had been oxidized during treatment. PEALD was successful in growing uniform and coalesced films of ZnO on both materials but destroyed the top layer of TMD by oxidation at the conditions tested. The interface of ZnO and 2D materials might be used in future nanoscale devices, and this study shows that it may be effectively controlled using different ALD methods.