The valved catheter assemblies described herein provide several advantages, including low cracking pressure for fluid infusion, greater cracking pressure for fluid aspiration, and reduction or elimination of dead space. In some embodiments, a valve of the catheter assembly has a conical shape, which provides different cracking pressures for infusion and aspiration. Also in some embodiments, a valve of the catheter assembly may include peripheral slits that enable fluid to flow around the perimeter of the valve during infusion, which helps to flush out fluid from around the valve.
