A theory is offered for the ballistic 4-terminal Josephson junction. The studied system consists of a mesoscopic two-dimensional normal rectangular layer which is attached on each side to the bulk superconducting banks (terminals). A relation is obtained between the currents through the different terminals, that is valid for arbitrary temperatures and junction sizes. The nonlocal coupling of the supercurrents leads to a new effect, specific for the mesoscopic weak link between two superconducting rings: an applied magnetic flux through one of the rings produces a magnetic flux in the other ring even in the absence of an external flux through the other one. The phase dependent distributions of the local density of Andreev states, of the supercurrents and of the induced order parameter are obtained. The “interference pattern” for the anomalous average inside the two-dimensional region can be regulated by the applied magnetic fluxes or the transport currents. For some values of the phase differences between the terminals, the current vortex state and the two-dimensional phase slip center appear.