The worker rollers of a teazing machine are rotationally driven by a device controlled so that they can be selectively driven either with slipping, by means of a belt drive 17, or without slipping, by means of a chain drive 19. As shown in Fig. 1, the shaft 1 of the teazing machine carries a drum 2 on the periphery of which are mounted nap rollers 3 and counter-nap rollers 4 rotatable about axes parallel to the shaft 1. Each roller 3, Fig. 2, is carried by a shaft 11 mounted by a bearing 12 in a bearing 13 secured to the drum 2. A hub 14 of a member 15 is screwed on to the shaft 11 and held thereon by a nut 21. A belt 17 passes over a part 16 of the member 15 and a chain 19 passes over a part 18 forming a triple-toothed wheel. The general configuration of the belt 17 and the chain 19 are indicated at 5, Fig. 1, and they are suitably driven by a pulley or chain wheel 6 freely mounted on the shaft 1. The belt 17 is always in position and when the chain 19 is in position the roller 3 is driven without slipping. When the chain 19 is removed the roller 3 is driven "flexibly", i.e. with slipping. The chain 19 may be removed by removing a demountable link therein, displacing a chain-tightener or by a mechanical device. In a second embodiment, Fig. 3, the belt 17 (not shown) is always in position on a member 31 screwed on to the shaft 11. A chain 33 passes over a toothed wheel 32 rotatably mounted by bearings 35, 36 on an extension 38 of the shaft 11. The wheel 32 may be rendered either fast or loose on the shaft 11 by an electro-magnet 51 with its winding 52 mounted through a needle bearing 53 upon the hub 44 of a member 45. Teeth (not shown) on the member 45 cooperate with teeth (also not shown) on a member 61 slidably mounted by teeth 62 upon teeth 63 cut in a member 64 secured to a drum 66 fixed to the wheel 32. When the magnet 51 is not excited permanent magnets 68 keep the member 61 disengaged from the member 45 but on excitation of the magnet 51 the member 45 attracts the member 61 to overcome the force of the magnets 68 so that the wheel 32 is fast about the shaft 11. For all rollers 3, conductors 57, Fig. 1, supplying each electromagnet are connected to two insulated conducting rings 69, 69a carried by the drum 2 and connected by brushes 70, 70a to a network R through a rheostat Rh for general regulation. In a further embodiment, Fig. 4, the belt 17 is omitted and a toothed wheel 71for a chain 72 is rotatably mounted through bearings 73, 74 on a sleeve 75 fixed to a fluted end of the shaft 11. Resilient canes 81, 82, 83 are positioned adjacent the bearings 73, 74, as shown. An electro-magnetic friction clutch comprises an armature 84 slidably mounted on and keyed to the sleeve 75. The magnetic circuit 86 enclosing the coil 87 is mounted on the sleeve 75 by a bearing 89, a resilient cane 97 being provided, and is secured against rotation relative to the drum 2. The armature 84 carries a rim or segments 98 of a material which rubs against a rim 101 secured to rim 102 provided with cooling fins 103. The rim 101 is rotationally bound by dowels 105 to a rim 106 fixed to the wheel 71. The rims 102, 106 are urged against each other by a spring 111. The flux of the magnet 86 presses the armature 84 against the rim 101 against the force of a spring comprising Belleville washers 114 between the armature 84 and a resilient cane 115. To drive the roller 3 without slip the strength of the current supplied to the coil 87 is a maximum. To obtain "flexible" control the current is reduced to reduce the driving torque effecting the connection between the wheel 71 and the shaft 11. In another embodiment, Fig. 5 (not shown), a chain 124 passes over a wheel 123 loosely mounted by a bearing 126 on an extension 125 of the shaft 11. The wheel 123 may be connected to the shaft 11 by a coupler 128 comprising a field magnet 131 carried by a collar 132 secured through a post 133 to the drum 2. The magnet 131 is lodged in an external pole piece 135 in the interior of which there is a rotatable pole piece 136 keyed to the extension 125. A two-part sleeve 141 is positioned between the pieces 135, 136 and is secured to member 145 fixed to the wheel 123. A magnetic powder is interposed between the piece 136 and the sleeve 141 and its viscosity varies according to the strength of the current supplied to the magnet 131 so that the driving torque between the shaft 11 and the wheel 123 is variable to drive the roller 3 with or without slip, as required. In a still further modification (not shown), each roller shaft is provided with a smooth loose belt pulley, a loose chain pinion and a double claw clutch enabling either the pulley or the pinion to be made fast on the shaft.