A catheter has a jacket (10, 11, 5) defining a lumen and a helical support (6). The catheter has a proximal portion (1) and a distal portion (3), the distal portion having for at least some of its length a corrugated outer surface. A transition portion has a flexural stiffness which is less than that of the distal portion and more than that of the proximal portion. The transition portion provides an optimum transition in flexural stiffness by way of features of the jacket including geometry of jacket corrugations (15), or overlapping tubular layers (1073, 1074). The distal end of the distal portion may have an extension of liner material folded over (1072, 1082) to provide a particularly soft tip. In other examples the liner is terminated (763) before the distal tip. The catheter is particularly suited to an aspiration device (1350) with a flow restrictor (1353) and the distal portion distal of the flow restrictor. An aspiration system (3500) may employ the catheter with a pump which dynamically applies negative or positive pressure to optimally aspirate a clot.
