Apparatus and methods for performing surgery within an organ or vessel are provided. A catheter is provided having a longitudinal axis and an end region carrying an end effector, the end region movable to a series of positions along the longitudinal axis and with an selectable orientation relative to the longitudinal axis. The catheter includes elements for stabilizing the end region of the apparatus within an organ or vessel, and for counteracting reaction forces developed during actuation of the end effector.