We have grown HgTe/CdTe superlattices by molecular beam epitaxy; barrier thicknesses were in the range from 15 to 91 A˚ and the well thickness was maintained at a constant value of 30 A˚. The infrared photoluminescence was investigated by means of Fourier transform infrared spectroscopy in the temperature range from 4.2 to 300 K. All superlattices showed pronounced photoluminescence at temperatures up to 300 K. To gain more detailed insight into the band structure of the HgTe/CdTe superlattices, band structure calculations were performed. The concept of the envelope function approximation was followed. Employing the transfer matrix method, the calculations were completed taking into account an eight bandk⋅pmodel. An important parameter in these calculations is the natural valence band offset (VBO) between the well and barrier materials. As a general trend, the value for the direct gap decreases with increasing VBO. The experimentally determined energies of the band gap are in reasonable agreement with the values obtained by the theoretical calculations. A comparison between theory and experiment shows that the observed transition energies are closer to calculations employing a large offset (350 meV) as opposed to a small VBO (40 meV).