The values of standard enthalpy of formation at 298.15 K and 1 atm for the double perovskites Sr2NiMoO6 and Sr2CoMoO6, measured by means of drop solution calorimetry, were found to be -2418.1 +/- 12.4 and -2422.9 +/- 9.6 kJ mol(-1), respectively. Heat capacity of Sr2NiMoO6 and Sr2CoMoO6 was measured between 2 and 370 K using relaxation and adiabatic calorimetry, and the enthalpy increments - between 373 and 1273 K using drop calorimetry. Low-temperature magnetic and higher-temperature structural phase transformations in Sr2NiMoO6 and Sr2CoMoO6 were discussed from the thermodynamic point of view. Specific heat (C-p), standard enthalpy (T0H(0)) and standard entropy (S-0) functions were derived from the experimental data for both double perovskites. The values of C-p, T0H(0) and S-0 at 298.15 K were determined to be 202.31 +/- 0.61 J mol(-1) K-1, 36.12 +/- 0.18 kJ mol(-1) and 231.3 +/- 1.6 J mol(-1) K-1 for Sr2NiMoO6, and 212.66 +/- 0.64 J mol(-1) K-1, 38.25 +/- 0.19 kJ mol(-1) and 244.4 +/- 1.7 J mol(-1) K-1 for Sr2CoMoO6, respectively. Additionally, using the thermodynamic data available, phase diagrams with respect to T and p(O2) showing stability limits and decomposition products were calculated for Sr2NiMoO6 and Sr2CoMoO6. Though the cobaltite's stability range is wider than nickelate's both in terms of T and p(O2), both complex oxides were found to be stable only at reasonably high temperatures and in oxidizing conditions, and metastable at low temperatures.