There has been a controversy about the reactivity of coal/char combustion under oxyfuel and air conditions. The conversions of NCP anthracite and DT bituminous coal chars were studied under different atmospheres, using simultaneous thermogravimetry and differential scanning calorimetry (TG-DSC). A model of the intrinsic reaction rate was developed to obtain the variable activation energy at different temperatures and char conversion ratios in terms of a TG-DSC curve only. In the endothermic stage, the chemisorption obeys the same mechanism in O-2/CO2, O-2/N-2 and O-2 atmospheres, in which the reaction order is about 0.48 in the nth-order model, while in CO2 is a zeroth-order reaction; both of them are not affected by coal rank. The chemisorption activation energy of CO2 is less than that of O-2. The chemisorption activation energies in O-2/CO2 are more than that in either 100% CO2 or 100% O-2, showing that both O-2 and CO2 compete for the same active sites. The char-O-2 chemisorption is inhibited by the char-CO2 chemisorption, resulting in a lower reactivity in O-2/CO2. Subsequently, in the exothermic stage, the NCP and DT char combustions obey different mechanisms, in which the reaction orders are 1.65 and 1, respectively. According to the significant differences in variable activation energies obtained from the TG and the DSC data, the char reaction can be divided into a multi-step chemisorption oxidation stage and a one-step burning stage. Compared with TG method, DSC method is more suitable for describing the reactive characteristics of the multi-step stage. The results show that the char-O-2/CO2 chemisorption partially shares common active sites with a complicated multi-step mechanism. The trends of variable activation energies with char conversion ratio at different O-2 concentration in O-2/CO2 are similar. The activation energy is not significantly affected by CO2, and is about 178 +/- 11 kJ/mol. The intrinsic reaction mechanisms of DT char combustion in O-2/CO2 and O-2/N-2 have no fundamental difference; however, the NCP char combustion is affected by both CO2 and oxygen partial pressure. (C) 2016 Elsevier Ltd. All rights reserved.