A bifurcated dual-balloon catheter apparatus for deploying one or more stents to a bifurcated vessel or for use in angioplasty procedures involving bifurcated vessels. The apparatus is particularly suited for bifurcated vessels of the type comprising a main branch from which a side branch extends therefrom. The apparatus has loon and a side branch balloon. A conduit is provided in the main branch balloon through which a portion of the side branch balloon extends. The first balloon is positionable within the main branch of the vessel while the distal portion of the second balloon is positionable within the side branch such that when the first and second balloons are inflated, the first balloon expands radially in the main branch while the distal portion of said second balloon maintains registration with the side branch by expanding radially therein.