We discuss the possible existence of current-voltage oscillations associated with discrete single-electron transfer in ultrasmall electrochemical solid-electrolyte contacts. Such oscillations arise from correlated single-electron transfer events between the metal electrode and solute reactant molecules close to the electrode, analogous to single-electron tunnelling (SET) in ultrasmall solid-state tunnel junctions. Electrochemical SET can be of two kinds. One is due to the small capacitance of the junction where electrostatic charging by a SET process blocks a subsequent SET step. This Coulomb blockade follows the pattern for solid-state junctions and requires very low temperatures which appear to be beyond the experimental limit at present. The other electrochemical SET phenomenon arises in ultrasmall tunnel electrode configurations and is associated solely with the discrete nature of the solvated molecular electron donor or acceptor. This effect could be observable at room temperature.