To cancel a thrust applied to a crankshaft without degrading a contact ratio of the gears, while retaining an essential function to reduce roll oscillation.

This roll-oscillation reducing apparatus includes two sub- flywheels 6a, 6b rotatably supported to the engine body through respective shafts 22a, 22b which are parallel to a crankshaft 11, and two helical gear sets for reverse-rotating the respective sub-flywheels 6a, 6b with respect to a main flywheel system at an increased speed. The moment of inertia Ii of each sub-flywheel 6a, 6b, speed increasing ratio ρi of each helical gear set, and angle of torsion θi of each helical gear set satisfy the relationship expressed by the following equation.