Abstract: The invention is directed to a very low-profile dilatation catheter having an inner tubular member with an inner lumen with a diameter of not more than 0.003 inch (0.076 mm) greater than the diameter of a guidewire disposed therein. Preferably, the inner diameter of the tubular member is less than 0.015 inch (0.381 mm). The inner member may be formed of a thin-walled tubing such as polyimide tubing having a wall thickness less than 0.003 inch (0.076 mm). Polyimide tubing is also preferably employed as the tubular member in low-profile steerable dilatation catheters wherein the guide elements thereof are fixed within the catheter.