In this paper, by analyzing the relationship between relative motions of the toroidal drive, the method for calculation of the sliding factors between the planet and stator or worm is given. Based on above-mentioned results, formulae of the friction coefficient between the planet and stator or worm under profile peak contact are presented. Based on EHL theory, formulae of the friction coefficient between the planet and stator or worm under hydrodynamic lubrication are introduced. Then, formulae of the friction coefficient between the planet and stator or worm under mixed friction are also introduced. Finally, by making use of the above-mentioned formulae, the friction coefficients between the planet and stator or worm under hydrodynamic lubrication are compared, and the dependences of them on parameters are discussed. Dependences of the friction coefficient between the planet and stator on the parameters under profile peak contact are given. And dependences of the friction coefficient between the planet and stator on the ratio of the film thickness to roughness under mixed friction are also discussed. These results are useful for manufacture and design of the drive.