We modeled two different mechanisms, a shunting conductance and a slow sodium inactivation, to test whether they could modulate the active propagation of a train of action potentials in a dendritic tree. Computer simulations, using a compartmental model of a pyramidal neuron, suggest that each of these two mechanisms could account for the activity-dependent attenuation and failure of the action potentials in the dendrites during the train. Each mechanism is shown to be in good qualitative agreement with experimental findings on somatic or dendritic stimulation and on the effects of hyperpolarization. The conditions under which branch point failures can be observed, and a few experimentally testable predictions, are presented and discussed.