(57) A centrifugal advance mechanism has a plurality of rotating weights (5) which travel under centrifugal force outwardly from an axis of a driving shaft (1) against the action of resilient means (11) urging the weights inwardly. The weights carry driving cam members (6) which interact by cam action with a driven cam member (8) which is thereby driven in rotation by the weights. The relative rotational position of the driven cam member (8) and the driving shaft (1) is thus determined by the radial position of the weights relative to the driving shaft (1). To improve performance of the mechanism under rapid rotational speed fluctuations, by means of the geometry of the weights (5) and the interacting cam surfaces of the driving and driven cam members (6,8), the inertial force of (a) the weights (5) and (b) the driven cam member (8) arising upon angular deceleration of the driving shaft (1) is controlled so as to have no outward action on the weights (5) over at least a part of the outward travel of the weights.