Hydrothermal reactions between aqueous Na2MoO4, Na2ESO3 (E=S, Se) and hydrazine monohydrate at 135 degrees C for 12 h produce phase-pure MoS2 and MoSe2 with good yield of about 90%. X-ray powder diffraction, chemical analysis and Xray photoelectron spectroscopy were used to characterize the structure and composition of the products annealed at 350 degrees C. Transmission electron microscopy images show that the samples of MoS2 and MoSe2 consist of nano-crystallites with average particle size of 4 nm and 7 nm, respectively.