The instant invention relates to a process and device for piecing on an open-end spinning device. Before the beginning of the piecing process the desired run-up curve for the fiber stream which is to be fed to the fiber collection surface and the acceleration curve of the fiber feeding device corresponding to this run-up curve are defined. During piecing the fiber feeding device is switched on and is driven in accordance with the defined acceleration curve. The fiber stream produced thereby is deflected and removed on its way between the fiber feeding device and a fiber collection surface. In this process the current actual values are calculated from the acceleration curve of the fiber feeding device and the fiber stream is again fed to the fiber collection surface when a predetermined desired value has been reached, before the fiber stream which is started by switching on the fiber feeding device has reached its full strength. In coordination therewith, a yarn is fed back to the fiber collection surface and is then continuously withdrawn from the fiber collection surface while the fibers are continuously incorporated.