A catheter having an elongated shaft which has a multilayered distal tip with a first layer formed of a polyimide first material and a second layer formed of a polymeric second material. In one embodiment the multilayered distal tip is a separate member, distal to the distal end of a proximal portion of the shaft. In another embodiment, the shaft has an outer tubular member, and a multilayered inner tubular member with a distal end which forms the multilayered distal tip of the shaft. In a presently preferred embodiment, the polyimide material is a thermoset polyimide. In one embodiment, the polymeric second material is a polyamide material.