Behaviour of electrolytes confined in cylindrical and slit pores are studied by computer simulations at the molecular level. Previous equilibrium and structural properties obtained by Monte Carlo techniques using the restrictive primitive model are discussed. Transport properties are calculated by the canonical molecular dynamics technique for ions with Lennard-Jones cores. Assuming an external electric potential, the chemical potential of individual ions can be balanced without the need for a grand canonical procedure. The mobility of the counterion is affected by the surface charge density. At a high surface charge, the mean square axial displacement of the counterion calculated is lower than the bulk value due to its high concentration near the charged wall.