For an air spinning frame, reluctance motors are provided for each spinning place to drive the pairs of rollers of the drafting unit, the drawing-off means, and the friction roller. Thereby, for the run-up of a spinning place, e.g., after a thread break, a specific frequency converter is provided. After reaching the stationary operating speed, a switch over onto a further frequency converter takes place, at which time, the corresponding reluctance motors of the other spinning places are driven in parallel. By the use of reluctance motors it can be done without a complex speed regulation means. A specific dimensioning of the reluctance motors permits a very fast run-up and a particularly good efficiency during the stationary operation.