The ability of point kinetics to describe dynamic processes in accelerator-driven systems (ADSs) is investigated. Full three-dimensional energy-space-time-dependent calculations, coupled with thermal and hydraulic feedback effects, are performed and used as a standard of comparison. Various transient accident sequences are studied. Calculations are performed in the range of keff = 0.9594 to 0.9987 to provide insight into the dependence of the performance on the subcritical level. Numerical experiments are carried out on a minor-actinide-loaded and lead-bismuth-cooled ADS. It is shown that the point kinetics approximation is capable of providing highly accurate calculations in such systems. The results suggest better precision at lower keff levels. It is found that subcritical operation provides features that are favorable from a point kinetics view of application. For example, reduced sensitivity to system reactivity perturbations effectively mitigates any spatial distortions. If a subcritical reactor is subject to a change in the strength of the external source, or a change in reactivity within the subcritical range, the neutron population will adjust to a new stationary level. Therefore, within the normal range of operation, the power predicted by the point kinetics method and the associated error in comparison with the exact solution tends to approach an essentially bounded value. It was found that the point kinetics model is likely to underestimate the power rise following a positive reactivity insertion in an ADS, which is similar to the behavior in critical systems. However, the effect is characteristically lowered in subcritical versus critical or near-critical reactor operation.