Abstract: An epicyclic transmission with steplessly-variable speed control includes a set of three planet wheels (46) which are in the form of tapered rollers of dual conicity and are supported for rotation by a planet carrier (34) driven by a drive shaft (28). The tapered planet wheels have a larger frusto-conical portion (48) in rolling contact with a governing annulus (58) which is locked for rotation and is displaceable axially, and a smaller frusto-conical portion (50) associated with a driven annulus (92) which rotates a driven shaft (102). The tapered planet wheels also have two axially-spaced bearing surfaces (52,54) in rolling contact with two corresponding bearing surfaces (136,138) of a freely-rotatable sun wheel in the form of a sleeve (122) coaxial with the drive shaft (FIG. 1).