The present work is part of a more extensive research carried out in Naples on cigarette combustion. Theoretical and modelling work highlighted the existence of a misdistribution of the gas flow across the cigarette cross-section, which results into locally variable conditions. As a consequence, oxygen-starving versus oxygen-rich conditions do establish in the pre-heat zone of the cigarette, where pyrolysis of cigarette components takes place. More specifically, oxygen-starving conditions should characterize the process of reaction front propagation in the inner part of the cigarette, close to its axis, while oxygen-rich conditions should establish at the cigarette periphery, close to the paper burn line. The present paper addresses the pattern and the kinetics of pyrolysis under inert and under oxidative conditions of three types of tobacco. The experimental work consists of non-isothermal thermogravimetric analysis at heating rates comprised between 5 and 20 °C/min and with different He–oxygen mixtures. Kinetic expressions for the rate of pyrolysis under inert and under oxidative conditions have been obtained for each ingredient investigated. Results, albeit obtained at sample heating rates smaller than those relevant to actual cigarette burning, highlight the profound differences arising under purely pyrolytic or oxy-pyrolytic conditions as regards the number of reaction steps, the rate, the temperature ranges and yields in solid versus gaseous products of thermal decomposition. The effect of inert/oxidative conditions on the chemical composition of the gaseous products of pyrolysis is discussed in a companion paper [O. Senneca, S. Ciaravolo, A. Nunziata, J. Anal. Appl. Pyrol. 78 (2007) 452].