A rotor for an electrical machine with one or a plurality of cooling ducts through which a cooling agent can flow. One end face of the rotor there is provided an annular space, bounded axially inwardly and radially outwardly and joined communicating with the cooling duct or ducts. A cover plate is provided, attached to the end face and bounding the annular space axially outwardly, having a central through-opening for introducing the cooling agent into the annular space.