The invention relates to a method for alternately supplying one of three outlets (C,D,E) of a cross-jet device (1) delivering a liquid to three washing agent- containers (41,42,43) in a washing machine (100), in particular a laundry washing or washing/drying machine, wherein the three containers (41,42,43) are in fluid communication with a tub of the washing machine (100), and wherein the cross-jet device (1) comprises a crossing chamber (X) to which a first and a second inlet (A,B) and three outlets (C,D,E) are afferent, which outlets (C,D,E) are in fluid communication with the three containers (43,41,42) and can be supplied alternately with said liquid depending on whether one or both of the inlets (A,B) are being supplied, and wherein the liquid supplied to the first inlet (A) is clean water taken from the water main, and the liquid supplied to the second inlet (B) is a wash liquid taken from the tub. The present invention also relates to a washing machine adapted to implement said method.