The paper is concerned with attenuated total reflection (ATR) in the reststrahl region. The superlattice is described by an effective-medium approximation, appropriate for long wavelengths, as a single uniaxial medium. Features in the ATRCUrVeS forp-polarised incident light are identified as corresponding to surface or guided-wave polaritons. Curves for s-polarisation show guided-wave modes but no surface modes.