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 (Cp), standard enthalpy (ΔT0H0) and standard entropy (S0) functions were derived from the experimental data for both double perovskites. The values of Cp, ΔT0H0 and S0 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 pO2 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 pO2, both complex oxides were found to be stable only at reasonably high temperatures and in oxidizing conditions, and metastable at low temperatures.