A washing and drying machine comprising: a tub; a water supply unit (13, 14, 16) configured to supply water into the tub; a drum rotatably installed in the tub to accommodate laundry; a motor configured to rotate the drum; a drying unit (40, 44, 45) disposed over the tub, configured to heat air discharged from the tub and circulate the heated air in such a manner that the laundry is dried; and a controller configured to control, during a drying process, the water supply unit and the motor in a manner that water supply is performed after a rotation speed of the drum has been increased to a predetermined speed, when a water supply condition occurs during execution of a drying process based on the drying unit (40, 44, 45), wherein the drying unit further includes: a heater and blowing fan configured to generate hot air for drying the laundry; a drying duct configured to direct the hot air into the drum; a circulation passage configured to allow air discharged from the tub to circulate in the drying duct; a filter installed at a suction inlet of the drying duct, configured to remove lint generated in the drying process; and a temperature sensor installed in the drying duct, configured to detect a temperature of the drying unit, wherein the controller is configured to control on/off operations of the heater according to the temperature of the drying unit (40, 44, 45) during execution of the drying process, and characterized in that the controller is further configured to determine the presence or absence of filter clogging using the number of heater-off occurrence in which the heater-off time is equal to or longer than a predetermined time, and to detect occurrence of a water supply condition in response to determining the presence of filter clogging, to control the motor such that the drum rotates at the predetermined speed, and to control the water supply unit (13, 14, 16) such that water is supplied to the filter in a manner that lint collected in the filter is removed. a tub; a water supply unit (13, 14, 16) configured to supply water into the tub; a drum rotatably installed in the tub to accommodate laundry; a motor configured to rotate the drum; a drying unit (40, 44, 45) disposed over the tub, configured to heat air discharged from the tub and circulate the heated air in such a manner that the laundry is dried; and a controller configured to control, during a drying process, the water supply unit and the motor in a manner that water supply is performed after a rotation speed of the drum has been increased to a predetermined speed, when a water supply condition occurs during execution of a drying process based on the drying unit (40, 44, 45), wherein the drying unit further includes: a heater and blowing fan configured to generate hot air for drying the laundry; a drying duct configured to direct the hot air into the drum; a circulation passage configured to allow air discharged from the tub to circulate in the drying duct; a filter installed at a suction inlet of the drying duct, configured to remove lint generated in the drying process; and a temperature sensor installed in the drying duct, configured to detect a temperature of the drying unit, a heater and blowing fan configured to generate hot air for drying the laundry; a drying duct configured to direct the hot air into the drum; a circulation passage configured to allow air discharged from the tub to circulate in the drying duct; a filter installed at a suction inlet of the drying duct, configured to remove lint generated in the drying process; and a temperature sensor installed in the drying duct, configured to detect a temperature of the drying unit, wherein the controller is configured to control on/off operations of the heater according to the temperature of the drying unit (40, 44, 45) during execution of the drying process, and characterized in that the controller is further configured to determine the presence or absence of filter clogging using the number of heater-off occurrence in which the heater-off time is equal to or longer than a predetermined time, and to detect occurrence of a water supply condition in response to determining the presence of filter clogging, to control the motor such that the drum rotates at the predetermined speed, and to control the water supply unit (13, 14, 16) such that water is supplied to the filter in a manner that lint collected in the filter is removed.