The bifurcating double stent apparatus (10) of the present invention comprises a generally cylindrical main stent (12), a generally cylindrical branch stent (15), which are shown as fully dilated in a subject main vessel (8), and a subject branch vessel (7). The main stent (12) is deployed prior to the branch stent (15) which is then aligned with the side opening (16) of the main stent (12), and attached at that location.