Aims. In this paper we study the Spitzer and TIMMI2 infrared spectra of post-AGB disc sources, both in the Galaxy and the LMC. Using the observed infrared spectra we determine the mineralogy and dust parameters of the discs, and look for possible differences between the Galactic and extragalactic sources. Methods. Modelling the full spectral range observed allows us to determine the dust species present in the disc and different physical parameters such as grain sizes, dust abundance ratios, and the dust and continuum temperatures. Results. We find that all the discs are dominated by emission features of crystalline and amorphous silicate dust. Only a few sample sources show features due to CO2 gas or carbonaceous molecules such as PAHs and C60 fullerenes. Our analysis shows that dust grain processing in these discs is strong, resulting in large average grain sizes and a very high crystallinity fraction. However, we do not find any correlations between the derived dust parameters and properties of the central source. There also does not seem to be a noticeable difference between the mineralogy of the Galactic and LMC sources. Even though the observed spectra are very similar to those of protoplanetary discs around young stars, showing similar mineralogy and strong grain processing, we do find evidence for differences in the physical and chemical processes of the dust processing.
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