A new junction sequence method for taking into account transport in a directed network of interconnected channels is suggested. It is a slight modification of the pathway and tree methods but is much more efficient. The requirements of the method in terms of computing time increases only linearly with the size of the network and sublinearly in terms of memory. The increased efficiency results from the introduction of a global order for the junctions in the network, which defines a sequence of the junctions such that transport at a junction only depends on preceding junctions but not on following junctions in the sequence. With this method the transport in the entire network can be calculated at one shot instead by superimposing a large number of pathways. The capabilities for some nonlinear effects like nonlinear sorption goes beyond the present pathway and tree methods. ¿ 2000 American Geophysical Union