1. The reversal potential of the slow outward current in Purkinje fibres varies with [K](o) in accordance with the expected potassium equilibrium potential. It is concluded that virtually all of this current is carried by potassium ions.2. The magnitude of the current is determined by two separable factors. The first factor is directly proportional to a variable obeying first-order voltage-dependent kinetics of the Hodgkin-Huxley type but with extremely long time constants. The time constants of this variable are extremely sensitive to temperature and the Q(10) over the range 26-38 degrees C is 6.3. The second factor shows inward-going rectification with a marked negative slope in the current-voltage relation beyond about 25 mV positive to the K equilibrium potential. The current-voltage relations measured at different values of [K](o) cross each other on the outward current side of the equilibrium potential.4. The changes in slow potassium current during pace-maker activity have been calculated. It is shown that the mechanism of the pace-maker potential differs in several important respects from that described by Noble's (1962) model. The negative slope in the current-voltage relation appears to be an important factor in generating the last phase of pace-maker depolarization.5. The role of the slow potassium current during the action potential and the consequences of the high temperature dependence of the kinetics are discussed.