To test the hypothesis of whether the intercalated discs represent a low resistance to diffusing ions, a method was developed to study the longitudinal diffusion of radioactive potassium (42K), tetraethylammonium ([14C]TEA), and the fluorescent dye Procion yellow (PY) in sheep and calf heart bundles. The method involved 1) loading the cells, 2) allowing the ions to diffuse for periods of 2-6 hr, 3) freezing the bundle in liquid air and cutting it into equal slices of 0.5 mm, 4) measuring the concentration of the ion in each slice. From the results, the diffusion of coefficients were considered to be due partially to the discs and partially to the myoplasm. The permeabilities of the nexal membranes were 7.68-10(-3), 1.27-10(-3), and 1.4-10(-6) cm/sec for 42K, 14C-TEA, and PY. These values are 9,600, 21,000, and 220 times more than the corresponding ones for the surface membrane. The disc resistance for potassium, the main intracellular charge carrier, was about 0.9 ohm cm2. From the van der Waals sizes of the ions, the diameter of the nexal pores has to be 10-15 A. It is concluded that the junctions between myocardial cells have low resistances and that propagation of action potentials is possible by local circuit currents.