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We have previously published several studies on the propagation of simulated action potentials (APs) of cardiac muscle and smooth muscle using the PSpice program. Those studies were done on single chains of five to ten cells in length to examine longitudinal propagation between the cells, either not connected by gap-junction (g.j) channels or connected by various numbers of channels. In addition, transverse propagation was examined between parallel chains (two to five chains) not connected by g.j. channels. In all those studies, the myocardial cells and smooth muscle cells (SMCs) were unintentionally somewhat hyperexcitable by virtue of the values inserted into the GTABLEs of the PSpice program. Because transmission of excitation from cell to cell occurred very well in the absence of g.j. channels, by virtue of the electric field (EF) generated in the narrow junctional clefts (negative cleft potential VJC), the present study was carried out, in which the cells were made hypo-excitable by altering the GTABLE values. Three levels of excitability of the cardiac cells and SMC were examined: 1) high; 2) intermediate; and 3) low. It was found that propagation of excitation, both longitudinally and transversely, can occur by the EF mechanism alone, even when the excitability of the cells was low. Therefore, the EF mechanism alone can account for propagation of excitation in cardiac muscles and smooth muscles that do not possess gap junctions. In those cases in which gap junctions do exist and are functioning, the EF mechanism would act in parallel and thereby increase the safety factor for conduction.