Cyclotron and intersubband resonances in HgTe quantum wells in the inverted band regime are studied by Fourier-transform spectroscopy. Metal-oxide-semiconductor field-effect transistors (MOSFETs) allow us to tune the electron density. In particular, we investigate filling factor dependent splittings of the cyclotron resonance in strong magnetic fields and a crossing of Landau levels of the conduction and valence subband. The experimental results are well described by a 6x6 k.p-model. (C) 1998 Elsevier Science B.V. All rights reserved.