In previous work, we showed that two-step biomass pyrolysis, consisting of a first low temperature step (T = 360 _C, so a low actual heating rate) until the mass loss of the solid reached approximately 50%, followed rapidly by a high temperature step (T > 600 _C, so a high actual heating rate) led to optimize charcoal yields with values of up to 40%. In this paper, we describe thermogravimetric analysis studies on eucalyptus wood and its three constituents, i.e. cellulose, xylan and lignin, in order to explain the phenomena behind these results. Two-step pyrolysis experiments were conducted in a TGA oven up to 900 _C with a first slow pyrolysis step at a low heating rate of 2 _Cmin_1, followed by a fast pyrolysis step with a heating rate of 100 _C min_1. Char yields from eucalyptus wood were increased from 18.8%, for the simple 2 _C min_1 pyrolysis, up to 22.8% when the heating rate change was operated at a temperature of 360 _C. Char yield from cellulose was also increased, though only very slightly, when the heating rate was changed in the 330-360 _C temperature range. Conversely, char yield obtained from xylan and lignin in two-step pyrolysis was always lower than that obtained by simple 2 _C min_1 pyrolysis. It appeared from this work that two-step pyrolysis of the eucalyptus sample could not be regarded and described as the result of the sum of the pyrolysis of its constituents. There was a matrix effect with interactions that promoted char formation during two-step pyrolysis.