To ensure that on-line measurements performed at a moving or stationary fiber structure, such as a fiber composite or a sliver, deliver useful and reproducible measuring values, the fiber structure, whether such be fiber composites or fiber slivers, must be compressed at the location where they pass a measuring location or site where there is accomplished the measurement with a commercially available measuring instrument or apparatus. According to the invention, there is selected as the measuring location or site a location of the fiber processing process where the fiber structure is compressed any way by virtue of the undergoing fiber processing process.