Excitation and deexcitation are fundamental phenomena in the electrophysiology of excitable cells. Both of them can be induced by stimulating a cell with intracellularly injected currents. With extracellular stimulation, deexcitation was never observed; only cell excitation was found. Why? A generic model with two variables (FitzHugh) predicts that an extracellular stimulus can both excite the cell and terminate the action potential (AP). Our experiments with single mouse myocytes have shown that short (2-5 ms) extracellular pulses never terminated the AP. This result agrees with our numerical experiments with the Beeler-Reuter model. To analyze the problem, we exploit the separation of time scales to derive simplified models with fewer equations. Our analysis has shown that the very specific form of the current-voltage (I-V) characteristics of the time-independent potassium current (almost no dependence on voltage for positive membrane potentials) is responsible here. When the shape of the I-V characteristics of potassium currents was modified to resemble that in ischemic tissues, or when the external potassium concentration (K0) is increased, the AP was terminated by extracellular pulses. These results may be important for understanding the mechanisms of defibrillation.