Long-duration particle image velocimetry measurements in rough-bed open-channel flows (OCFs) reveal that the pre-multiplied spectra of the streamwise velocity have a bimodal distribution due to the presence of large- and very-large-scale motions (LSMs and VLSMs, respectively). The existence of VLSMs in boundary layers, pipes and closed channels has been acknowledged for some time, but strong supporting evidence for their presence in OCF has been lacking. The data reported in this paper fill this gap. Length scales of the LSMs and VLSMs in OCF exhibit different scaling properties; whereas the streamwise length of the LSM scales with the flow depth, the VLSM streamwise length does not scale purely with flow depth and may additionally depend on other scales such as the channel width, roughness height or viscous length. The transverse extent of the LSMs was found to increase with increasing elevation, but the VLSM transverse scale is anchored around two flow depths. The origin and nature of LSMs and VLSMs are still to be resolved, but differences in their scaling suggest that VLSMs in rough-bed OCFs form independently rather than as a spatial alignment of LSMs.