A dual cavity toroidal type CVT includes two toroidal transmission units (31, 32). A torque delivery shaft (27) carries a first input disc (35) and a second input disc (36) coaxially for a unitary rotation. A third common output disc (37) between the first and second input discs (35, 36) has an output gear (73) fixedly attached to an outer periphery thereof. Radial bearings (39, 40) received in peripheral grooves (27a, 27b) of the torque delivery shaft (27) are in rolling contact with a central opening defining wall of the third common output disc (37). Two supports (41, 42) are fixedly attached to a transmission casing (21) and bear thrust load tending to tilt the third common output disc (37) from a predetermined normal upright position, thereby to hold the third common output disc (37) in the predetermined normal upright position.