The invention is directed to a method for at least partially removing a contamination layer (15) from an optical surface (14a) of an EUV-reflective optical element (14) by bringing a cleaning gas into contact with the contamination layer. In the method, a jet (20) of cleaning gas is directed to the contamination layer (15) for removing material from the contamination layer (15). The contamination layer (15) is monitored for generating a signal indicative of the thickness of the contamination layer (15) and the jet (20) of cleaning gas is controlled by moving the jet (20) of cleaning gas relative to the optical surface (14a) using this signal as a feedback signal. A cleaning arrangement (19 to 24) for carrying out the method is also disclosed. The invention also relates to a method for generating a jet (20) of cleaning gas and to a corresponding cleaning gas generation arrangement.