The 23 920 cm-1, 21 950 cm-1, and 17 840 cm-1 emission bands of KrD have been analysed successfully as transitions from the 8p, 7p, and 6p Rydberg complexes to the lowest bound state, 2Σ. It was found that the structure of these states corresponds to a special case of l uncoupling with a Coriolis-like linear dependence of the case (d) electron-rotation energies on the quantum number R. The structure of the lowest member of the series, the 5p(2Σ, 2Π) complex, has been obtained from the simultaneous analysis of the 5 050 cm-1 and 5 800 cm-1 emission bands as transitions from the 4d2Π case (b) upper state to the 5p2Σ and 5p2Π components of the complex. The latter are widely split, E Π - E Σ = 735 cm-1, due to electronic interactions and are further distorted by strong spin-orbit interactions. The 5p(2Σ, 2Π) complex corresponds to the p complex of ArD studied recently by Dabrowski, I., Dilonardo, G., Herzberg, G., Johns, J. W. C., Sadowskii, D. A., and Vervloet, M., 1992, J. chem. Phys., 97, 7093.