Beverage dispensing machine, including: - a first milk reservoir, in which regular milk is stored, - a second milk reservoir, in which lactose-free milk or a lactose-free milk substitute is stored, - a first milk supply duct, which connects said first milk reservoir to a first inlet of a three-way joint, a first shut-off valve being arranged on said first milk supply duct between said first milk reservoir and said three-way joint 40. - a second milk supply duct, which connects said second milk reservoir to a second inlet of said three-way joint, a second shut-off valve being arranged on said second milk supply duct between said second milk reservoir and said three-way joint, - a milk delivery duct, which connects the outlet of said three-way joint to an outlet spout, a milk pump being arranged on said milk delivery duct between said three-way joint and said outlet spout, wherein said beverage dispensing machine is equipped with a control unit and with a user interface for selection of a desired beverage, - the control unit being programmed to carry out a regular milk delivery cycle, in which it sends a control signal for opening said first shut-off valve and closing said second shut-off valve and for starting said milk pump, whereby regular milk is drawn from said first milk reservoir and conveyed through said first milk supply duct and said milk delivery duct to said outlet spout; - the control unit being further programmed to carry out a lactose-free delivery cycle, in which it sends a control signal for closing said first shut-off valve and opening said second shut-off valve and for starting said milk pump, whereby lactose-free milk or the lactose-free milk substitute is drawn from said second milk reservoir and conveyed through said second milk supply duct and said milk delivery duct to said outlet spout; and - the control unit being further programmed to carry out a rinsing cycle, in which it sends a control signal for causing a rinsing fluid to flow through said milk delivery duct to said outlet spout; whereby lactose-free milk or the lactose-free milk substitute stored in said second milk reservoir is used as rinsing fluid and during said rinsing cycle said control unit sends a control signal for closing said first shut-off valve and opening said second shut-off valve and for starting said milk pump, whereby lactose-free milk or the lactose-free milk substitute is drawn from said second milk reservoir and conveyed through said second milk supply duct and said milk delivery duct to said outlet spout. - a first milk reservoir, in which regular milk is stored, - a second milk reservoir, in which lactose-free milk or a lactose-free milk substitute is stored, - a first milk supply duct, which connects said first milk reservoir to a first inlet of a three-way joint, a first shut-off valve being arranged on said first milk supply duct between said first milk reservoir and said three-way joint 40. - a second milk supply duct, which connects said second milk reservoir to a second inlet of said three-way joint, a second shut-off valve being arranged on said second milk supply duct between said second milk reservoir and said three-way joint, - a milk delivery duct, which connects the outlet of said three-way joint to an outlet spout, a milk pump being arranged on said milk delivery duct between said three-way joint and said outlet spout, wherein said beverage dispensing machine is equipped with a control unit and with a user interface for selection of a desired beverage, - the control unit being programmed to carry out a regular milk delivery cycle, in which it sends a control signal for opening said first shut-off valve and closing said second shut-off valve and for starting said milk pump, whereby regular milk is drawn from said first milk reservoir and conveyed through said first milk supply duct and said milk delivery duct to said outlet spout; - the control unit being further programmed to carry out a lactose-free delivery cycle, in which it sends a control signal for closing said first shut-off valve and opening said second shut-off valve and for starting said milk pump, whereby lactose-free milk or the lactose-free milk substitute is drawn from said second milk reservoir and conveyed through said second milk supply duct and said milk delivery duct to said outlet spout; and - the control unit being further programmed to carry out a rinsing cycle, in which it sends a control signal for causing a rinsing fluid to flow through said milk delivery duct to said outlet spout; whereby lactose-free milk or the lactose-free milk substitute stored in said second milk reservoir is used as rinsing fluid and during said rinsing cycle said control unit sends a control signal for closing said first shut-off valve and opening said second shut-off valve and for starting said milk pump, whereby lactose-free milk or the lactose-free milk substitute is drawn from said second milk reservoir and conveyed through said second milk supply duct and said milk delivery duct to said outlet spout.