Out-of-equilibrium systems exhibit domain walls between different states. These walls, depending on the type
of connected states, can display rich spatiotemporal dynamics. In this Rapid Communication, we investigate
the asymmetrical counterpropagation of fronts in an in-plane-switching cell filled with a nematic liquid crystal.
Experimentally, we characterize the different front shapes and propagation speeds. These fronts present dissimilar
elastic deformations that are responsible for their asymmetric speeds. Theoretically, using a phenomenological
model, we describe the observed dynamics with fair agreement.