Although drugs that block the fast sodium current in the heart have been in wide use for the last 40 years the actual mechanisms behind their therapeutic actions are not well understood. A new hypothesis for the action of such drugs will be presented in this talk. The effect of these drugs on isolated cells, represented by ordinary differential equations, will be compared to effects in a chain of cells. Predictions from numerical computations will be compared to experimental results. A theoretical basis for the propagation phenomena will be discussed.