The thermal stability of a series of cobalt and nickel molybdates (AMoO4 . nH(2)O, alpha-AMo(4), and beta-AMoO(4); A = Co or Ni) was examined using synchrotron-based time-resolved X-ray powder diffraction (XRD). The results of X-ray absorption near-edge spectroscopy (XANES) indicate that the Co and Ni atoms are in octahedral sites in all these compounds, while the coordination of Mo varies from octahedral in the alpha-phases to tetrahedral in the beta-phases and hydrates. Upon heating of AMoO(4) . nH(2)O, evolution-of gaseous water was seen at two different temperature ranges : 100-200 degrees C for reversibly bound H2O; 200-400 degrees C for H2O from the crystal structure. The results of time-resolved XRD show a direct transformation of the hydrates into the beta-AMoO(4) compounds (following a kinetics of first order) without any intermediate phase. This is probably facilitated by the similarities that AMoO4 . nH(2)O and beta-AMoO(4) have in their structural and electronic properties. The XRD experiments show that the alpha-AMoO(4)-->beta-AMoO(4) transitions occur at much higher temperatures than the hydrate --> beta-AMoO(4) transformations (Delta T approximate to 150 degrees C in CoMoO4 and 280 degrees C in NiMoO4). The activation energy for the alpha-NiMoO4 --> beta-NiMoO4 transition is similar to 40 kcal/mol larger than that for the NiMoO4 . nH(2)O --> beta-NiMoO4 + nH(2)O reaction. The larger activation energy reflects the change in the coordination of Mo (O-h --> T-d) that occurs during the alpha --> beta transition. The K- and L-edges of Co in XANES spectra indicate that there are no big variations in the electronic properties of this metal when comparing CoMoO4 . nH(2)O, alpha-CoMoO4, and beta-CoMoO4. The same is valid for the electronic properties of Ni in the nickel molybdates. In contrast, the L-2,L-3-edges of Mo show large changes in the splitting of the Mo 4d orbitals as the coordination of this metal varies from octahedral (alpha-phases) to tetrahedral (beta-phases and hydrates). The features near the threshold in the O K-edge spectra track very well the splitting of the Mo 4d orbitals in tetrahedral and,octahedral fields and can be very useful for probing the local symmetry of Mo atoms in molybdenum oxides.