The range of speed ratios available from a simple two-path, variable-ratio transmission is increased by adding a two-speed gear train and a pair of clutches. Two phases of operation minimize the torque demand on the variable ratio elements; transfer between these phases is effected by clutches engaged when unloaded and at a synchronous speed. In consequence, no speed or torque discontinuity occurs when engaging or freeing a clutch. Dimensionless analytical relations describing the transmission are developed.