Conductance responses of some sintered samples of SnO2 prepared in the form of thick films are studied in the H2S concentration range from 0.1 to 50 ppm in dry synthetic air and also in ambient containing different levels of humidity. The experiments are carried out at equilibrium conditions, by allowing the samples to stabilize at constant temperatures, and at non-equilibrium conditions, by quickly cooling the samples from an initial temperature of around 400-degrees-C to a final temperature of around 150-degrees-C. Continuous temperature-cycling experiments are also performed, with a cycle length of (60 + 60) seconds between the two temperatures, in order to study the feasibility of using the conductance response under non-equilibrium conditions for continuous H2S sensing. The effect of some additives in SnO2 on the conductance response under equilibrium and non-equilibrium conditions is also studied.