An electrically rotating machine, includes a rotor and a stator, the rotor and/or the stator including a laminated core, with an air gap being formed between the rotor and the stator, said rotor having axially and radially extending cooling paths in flow communication with each other and in flow communication with radially extending cooling paths of the stator via the air gap, wherein the radially extending cooling paths of the stator are respectively axially aligned with the radially extending cooling paths of the rotor; at least one fan for conducting an air flow through the axially and radially extending cooling paths of the rotor, the air gap and the cooling paths of the stator, wherein the air gap has at least one constriction defined by sheets of the laminated core of the rotor having an outer radius greater than remaining ones of the sheets of the laminated core of the rotor and/or by sheets of the laminated core of the stator having a smaller inner radius than remaining ones of the sheets of the laminated core of the stator.