The dynamics of electroporation in biological cells subjected to nanosecond, high-intensity pulses are studied based on a coupled scheme involving both the current continuity and Smoluchowski equations. A new distributed network model, that includes dynamic conductivities of cell membranes and substructures, is introduced for evaluations of transmembrane potential. It is shown that subcellular structures could be affected through nanosecond pulses, and that, despite the high field intensity, the processes remain nonthermal. As an example of selectivity, differences in cell responses between normal and malignant (Farage) tonsillar B-cells are compared and discussed. It is shown that ultrashort, high-intensity electric pulses could damage cancer cells. Finally, the model predicts that it is possible to target the inner mitochondrial membrane (i.e., selectivity at the organelle level), in keeping with recent experimental observations.