We apply equilibrium and nonequilibrium molecular dynamics simulations to study the dynamic properties of electrolytes in nanopores. The realistic primitive model and the restrictive primitive model widely used in the statistical mechanics of liquid-state theory are applied to model the electrolytes. The electrolytic ions are immersed in water, treated in this work as either a dielectric continuum ignoring the size of solvent molecules or a macroscopic dielectric continuum (polar property) plus neutral soft spheres, and the aqueous electrolyte is put in a confined space. To simulate a condition mimicking closely processes of practical interest and yet maintaining the simulation computationally manageable, we consider an infinitely long and uncharged cylindrical tube. The equilibrium property of the self-diffusion coefficient D and the nonequilibrium property of electric conductivity sigma are computed in terms of electrolyte concentration, particle size, and cylindrical pore radius. The simulation results for the continuum solvent restrictive primitive model and continuum solvent primitive model show normal behavior for D versus pore radius R at ionic concentration 0.1M -i.e., D decreases with decreasing R -display an R independence of D at a certain threshold concentration and undergo an anomalous increase in D with reducing R at a lower value 0.025 M. The mechanism of the anomaly at the ionic concentration 0.025 M was sought for and interpreted in this work to arise from the energetic and entropic factors. Our simulated data of sigma at this same concentration follow the same trend as D. To delve further into the transport properties, we perform simulation studies for the discrete solvent primitive model and make a detailed analysis of the characteristic of the ion radial density functions. Comparison of the latter functions with those in the continuum solvent primitive model sheds light on the simulated diffusion coefficient within the context of discrete solvent primitive model which is about two orders of magnitude less. This difference in D is naturally attributed to the solvent effect. Similar disparities were reported by others for the discrete and continuum restrictive primitive models.