The photodissociation dynamics of HF and DF, following A (1)Pi <-- X (1)Sigma(+) electronic excitation, are examined using time-dependent wave packet techniques. The calculations are based on new multireference configuration interaction calculations of the potential energy curves and complete active space self-consistent field calculations of the off-diagonal spin-orbit coupling matrix elements. The calculated branching fraction for the formation of excited state fluorine, F*(P-2(1/2)), following excitation from the ground vibrational state (v=0) of HF, agrees well with the value of 0.41 +/- 0.08 measured experimentally at 121.6 nm by Zhang [J. Chem. Phys. 104, 7027 (1996)]. Predictions are made for the excited spin-orbit state branching fraction for both HF and DF over a wide range of photon excitation energies. The results for HF and DF are discussed in context with the corresponding results for the photodissociation of HCl and DCl.