A supercharging arrangement for an internal combustion engine comprising: a supercharger having a first rotational drive input shaft ; a transmission having a second rotational drive input shaft to receive drive from the internal combustion engine via a pulley at a speed ratio (R1), and a rotational drive output shaft connected to the first rotational drive input shaft of the supercharger , wherein the transmission includes a variator operatively connected between the second rotational drive input shaft and the rotational drive output shaft of the transmission , which variator has an output shaft that is driven at an operating ratio (Rv) from a third input shaft coming from a fixed ratio stage (R2) of the transmission; and a control system that operates to cause the engine to deliver an amount of torque in response to a state of an operating control, wherein the control system is operative to set the operating ratio (Rv) of the variator to a variator ratio request and to adjust the operating ratio (Rv) of the variator to ensure that a rate at which the supercharger speed changes does not exceed a predetermined limit, and to ensure that the torque that is applied to the output of the engine or to the variator does not exceed a threshold, and wherein the control system is operative to calculate an air pressure at an outlet of the supercharger to generate a supercharger air pressure request based on the state of the operating control, calculate a mass air flow required to achieve the supercharger air pressure request at a current speed of the internal combustion engine, determine a speed of the supercharger to achieve the calculated mass air flow, generate a supercharger speed request based on the determined speed of the supercharger, and calculate the variator ratio request based on the supercharger speed request. a supercharger having a first rotational drive input shaft ; a transmission having a second rotational drive input shaft to receive drive from the internal combustion engine via a pulley at a speed ratio (R1), and a rotational drive output shaft connected to the first rotational drive input shaft of the supercharger , wherein the transmission includes a variator operatively connected between the second rotational drive input shaft and the rotational drive output shaft of the transmission , which variator has an output shaft that is driven at an operating ratio (Rv) from a third input shaft coming from a fixed ratio stage (R2) of the transmission; and a control system that operates to cause the engine to deliver an amount of torque in response to a state of an operating control, wherein the control system is operative to set the operating ratio (Rv) of the variator to a variator ratio request and to adjust the operating ratio (Rv) of the variator to ensure that a rate at which the supercharger speed changes does not exceed a predetermined limit, and to ensure that the torque that is applied to the output of the engine or to the variator does not exceed a threshold, and wherein the control system is operative to calculate an air pressure at an outlet of the supercharger to generate a supercharger air pressure request based on the state of the operating control, calculate a mass air flow required to achieve the supercharger air pressure request at a current speed of the internal combustion engine, determine a speed of the supercharger to achieve the calculated mass air flow, generate a supercharger speed request based on the determined speed of the supercharger, and calculate the variator ratio request based on the supercharger speed request. <EOS>