A method of making catheters is disclosed in which the wall of the catheter has a porous structure for carrying additional agents, such as therapeutic agents, diagnostic agents and/or device enhancements. The method includes applying a base polymer material and an inert material over the outer surface of a core, and curing or consolidating the base polymer material to form a catheter having a porous polymer layer with the inert material contained within the pores thereof. The inert material can be applied with the base polymer material or in a separate step after the base polymer material has been partially cured or consolidated to form the porous polymer layer. Additional agents can be mixed with the inert material before it is applied to the catheter, or can be applied to the porous polymer layer of the catheter in a separate step after the inert material is removed therefrom.
