We have previously determined an analytical ab initio 6-dimensional potential energy surface for the HF dimer [P. R. Bunker, P. Jensen, A. Karpfen, M. Kofranek, and H. Lischka, J. Chem. Phys. 92, 7432-7440 (1990)], and used it in the calculation of the intensities and wavenumbers of intramolecular HF stretching excited states [P. Jensen, P. R. Bunker, A. Karpfen, M. Kofranek, and H. Lischka, J. Chem. Phys. 93, 6266-6280 (1990)]. In the present paper we extend the calculation to the v1 + v2 = 4 overtone bands around 15 000 cm-1. We find that the most intense of these bands will be the third overtone of the free HF stretch (v1 = 4, v2 = 0) which we calculate to be at 14 676 cm-1 with a transition moment close to that of the third overtone of the monomer. In a separate ab initio calculation the D2h saddle point for H-atom exchange, on the dimer potential energy surface, has been determined to be at an energy of about 15 000 cm-1, and therefore H-atom exchange effects may be observable in the v1 + v2 = 4 bands. © 1991.