We have used density functional theory to investigate hydrogen desorption from SiGe alloy surfaces, and the effect of Ge alloying on the kinetics of hydrogen desorption via the prepairing and interdimer mechanisms. We find that the calculated activation barriers of the prepairing mechanism are affected by the surface atom bonded to the desorbing hydrogen atoms. On the other hand, our calculations show that the activation barrier for hydrogen desorption via the 2H interdimer mechanism is affected by all four surface atoms of the two neighboring dimers. For the 4H interdimer mechanism, we have shown that the activation barrier for hydrogen desorption is not significantly higher than the endothermicity of hydrogen desorption. We also find that the calculated activation barriers of the interdimer mechanisms are generally lower than those of the prepairing mechanism. In addition, our calculations show that surface Ge atoms on neighboring dimers on SiGe alloy surfaces have a minor effect on the calculated activation barriers of both the prepairing and interdimer mechanisms, which indicates that the effect of Ge alloying on hydrogen desorption is local in nature. We also discuss the effects of cluster size and constraints on the calculated reaction energies and activation barriers of hydrogen desorption via the two mechanisms.