International audienceWe present observations of the young multiple system UX Tauri to look for circumstellar disks and for signs of dynamical interactions. We obtained SPHERE/IRDIS deep differential polarization images in the J and H bands. We also used ALMA archival CO data. Large extended spirals are well detected in scattered light coming out of the disk of UX Tau A. The southern spiral forms a bridge between UX Tau A and C. These spirals, including the bridge connecting the two stars, all have a CO (3-2) counterpart seen by ALMA. The disk of UX Tau C is detected in scattered light. It is much smaller than the disk of UX Tau A and has a major axis along a different position angle, suggesting a misalignment. We performed Phantom SPH hydr...