A dilatation or other similar catheter for intraluminal use which has an elongated shaft and an inflatable member or section on the distal extremity of the catheter shaft which has multiple working sections, a first working section which elastically expands upon inflation to a first pressure within a first pressure range and a second working section which elastically expands upon inflation to a second pressure within a second pressure range which is at least in part higher than the first pressure range. The first working section may be inflated to secure the catheter within the body lumen and then the second working section may be inflated to dilatate the body lumen.