A cooling arrangement for an electric machine (1, 1a, 1b) includes a rotatably mounted rotor shaft (2). A rotatably mounted hollow shaft (11) is mounted coaxially to the rotor shaft (2) and rotationally fixed to the rotor shaft (2). A hollow shaft inner side (12) is spaced apart from a rotor shaft outer side (5) in a radial direction (R) in order to form an annular gap (14). At least one cooling duct for a cooling lubricant includes a hollow shaft duct (18), a feed duct (20), and an outlet duct (25). The feed duct (20) opens into the hollow shaft duct (18) in order to feed the cooling lubricant to the hollow shaft duct (18). The outlet duct (25) extends from the hollow shaft duct (18) to the annular gap (14) in order to release the cooling lubricant from the hollow shaft duct (18) into the annular gap (14).