Abstract: An infusion catheter for delivering drugs or other agents to selected sites in an organism, such as a human. In an alternate embodiment, a catheter system is disclosed having an infusion catheter and a pump that may be implanted or disposed outside the organism. In either embodiment, the free end of the catheter bears a rounded tip that has at least one elution hole for discharging an agent or drug to a selected site. The catheter has a tubular inner liner that is integral with the tip. The inner liner and tip are formed from a drug compatible polymeric material that is relatively nonporous and unreactive with the agent to be infused. A biocompatible flexible elastomeric tubular jacket surrounds the inner liner and a portion of the tip excluding that portion containing the elution hole or holes.