Contact inhibition of locomotion (CIL), a migratory mechanism, first introduced by Abercrombie and Heaysman in 1953 is now a fundamental driving force in developmental, repair and disease biology. Much of what we know of CIL stems from studies done on 2D substrates which are unable to provide the essential biophysical cue of fibrous extracellular matrix curvature. Here we inquired if the same rules are applicable for cells attached to and migrating persistently on suspended and aligned ECM-mimicking nanofibers. Using two elongated cell shapes (spindle attached to one fiber, and parallel attached to two fibers), we quantitate CIL rules for spindle-spindle, parallel-parallel and spindle-parallel collisions. Two approaching spindles do not repolarize upon contact but rather continue to migrate past one another. Contrastingly, approaching parallel cells establish distinct CIL, with only one cell repolarizing upon contact followed by migration of both cells as a cohesive unit in the repolarization direction. Interestingly, for the case of spindle and parallel cell collision, we find the parallel cell to shift the morphology to that of spindle and continue persistent movement without repolarization. To account for effect of cell speed, we also quantitate CIL collisions between daughter and non-dividing cells. While spindle-spindle collisions result in cells still walking by, for parallel-parallel collisions, we capture rare events of a daughter cell pushing the non-dividing cell. With increasing population numbers, we observe formation of cell streams that collapse into spheroids. Single cells are able to invade along fibers from the spheroids and are then subject to same CIL conditions, thus providing a platform with cyclic CIL. The presented coupling of experimental and analytical framework provides new insights in contextually relevant CIL and predictive capabilities in cell migration decision steps.