An electric machine includes a housing for accommodating a rotatably supported rotor and a stationary stator, and a cooling device for cooling heat-generating components of the rotor and the stator. The cooling device includes a closed-flow system having an evaporator disposed in the housing, a condenser disposed outside the housing at a geodetically higher location, and a closed tube assembly, which connects the condenser and the evaporator, for circulating a coolant using a thermosiphon effect as a result of a difference in density between vapor and liquid portions of the coolant. The closed-flow system contains a liquid-vapor mixture of the coolant in a saturated state and includes a first tube for conducting coolant to the evaporator and a second tube for conducting coolant away from the evaporator. The first tube has hereby a cross section which is smaller than a cross section of the second tube.