The magnetostatic interaction between magnetic domain walls (DWs) in adjacent nanotracks has been shown to produce strong inter-DW coupling and mutual pinning. In this paper, we have used electrical measurements of adjacent spin-valve nanotracks to follow the positions of interacting DWs. We show that the magnetostatic interaction between DWs causes not only mutual pinning, as observed till now, but that a travelling DW can also induce the depinning of DWs in near-by tracks. These effects may have great implications for some proposed high density magnetic devices (e.g. racetrack memory, DW logic circuits, or DW-based MRAM).