Membrane electrical properties were measured in sheep cardiac Purkinje fibers, having diameters ranging from 50 to 300/µm. Both membrane capacitance and conductance per unit area of apparent fiber surface varied fourfold over this range. Membrane time constant, and capacitance per unit apparent surface area calculated from the foot of the action potential were independent of fiber diameter, having average values of 18.8 4- 0.7 ms, and 3.4 ± 0.25 µF/cm2, respectively (mean ± SEM). The conduction velocity and time constant of the foot of the action potential also appeared independent of diameter, having values of 3.0 ± 0.1 m/s and 0.10 ± 0.007 ms. These findings are consistent with earlier suggestions that in addition to membrane on the surface of the fiber, there exists a large fraction of membrane in continuity with the extracellular space but not directly on the surface of the fiber. Combining the electrical and morphological information, it was possible to predict a passive length constant for the internal membranes of about I00/-m and a time constant for charging these membranes in a passive 100-µm fiber of 1.7 ms. © 1975, Rockefeller University Press., All rights reserved.