Measurements of transient membrane potential after current switch-off have been used to study the electrochemical and other transport properties of nanoporous track-etched membranes (pore diameter of 24 nm) in KCl solutions of various concentrations. Due to their identical straight cylindrical pores within the nanorange, those membranes are a suitable object for the studies of fundamentals of nanofluidics. We have developed a theory, which enabled us to interpret the transients of membrane potential in terms of such properties as the ion transport numbers, the membrane diffusion permeability, and the specific chemical capacity. The fitted values have been further interpreted within the scope of the space-charge model and revealed good self-consistency. The dependence of fitted values of the surface charge density on salt concentration was in agreement with the mechanism of fixed charge formation due to the dissociation of weakly acidic groups, and the surface charge density corresponded well to the measurements by an independent method. Thus, our measurements have revealed a quantitative applicability of standard space-charge model to the description of electrochemical phenomena and electrolyte diffusion in straight cylindrical pores of tens of nanometers in diameter. Proceeding from our data, we could estimate the limiting current densities for our nanofluidic system. They have turned out to be more than 2 orders of magnitude lower than usually encountered in microfluidic systems with electro-osmotic fluid delivery. That finding may point to a considerable handicap in the application of such nanofluidic elements in microsystems.