  We describe recent results obtained by G. Barles, P. Cardaliaguet, R. Monneau
and the author recently. They are concerned with nonlocal Eikonal equations
arising in the study of the dynamics of dislocation lines in crystals. These
equations are nonlocal but also non monotone. We use a notion of weak solution
to provide solutions for all time. Then, we discuss the link between these weak
solutions and the classical viscosity solutions, and state some uniqueness
results in particular cases. A counter-example to uniqueness is given.
