A single- or multiple-head embroidery machine has stitch-forming tools which are formed in each case by a thread-guiding needle that interacts with a double-lock-stitch gripper to form stitches, and also has a feed device for obtaining relative movements between the embroidery material and the stitch-forming tools. The relative movements occur depending on the movements of the needle. In order to avoid a temporal overlap between the stitch-forming phase and the feed movement of the embroidery material, the double-lock-stitch gripper rotates at a rotational speed which corresponds to n times the rotational speed of the machine main shaft, wherein “n” is an integer greater than the number “2”.