Simulations of the collapse and fragmentation of turbulent molecular clouds and dense young clusters show that encounters between disc-surrounded stars are relatively common events which should significantly influence the resulting disc structure. In turn this should alter the accretion rate of disc matter onto the star and the conditions under which planet formation occurs. Although the effects of star-disc encounters have been previously investigated, very little is known about encounters where both stars are surrounded by discs. In this paper encounters of such disc-disc systems are studied quantitatively. It is found that for low-mass discs ($M_D$= 0.01 $M_sun$) the results from star-disc encounters can be straightforwardly generalized to disc-disc encounters as long as there is no mass transport between the discs. Differences to star-disc encounters occur naturally where significant amounts of matter are transported between the discs. In this case it is found that although the mass distribution does not change significantly, matter caught onto highly eccentric orbits is transported surprisingly far inside the disc. The captured mass partly replenishes the disc, but has a much lower angular momentum. This can lead to a reduction of the angular momentum in the entire disc and thus considerably increased accretion shortly after the encounter as well as in the long term.
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