We provide a convergence result for numerical schemes approximating nonlocal front propagation equations. Our schemes are based on a recently investigated notion of a weak solution for these equations. We also give examples of such schemes, for a dislocation dynamics equation, and for a FitzHugh-Nagumo type system. which, in the level-set approach for front propagation (see [19, 18, 12] for a complete overview of this method), describe the movement of a family {K(t)} t∈[0,T ] of compact subsets

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... of R N such that Here u t , Du and D 2 u denote, respectively, the time derivative, space gradient and space Hessian matrix of u, while 1 A denotes the indicator function of any set A. The function H corresponds to the velocity of the front. In our setting, it depends not only on local properties of the front, such as its position, the time, the normal direction and its curvature matrix, but also, at time t, on the family {K(s)} s∈ [0,t] itself. This nonlocal dependence is carried by the notation H[1 {u≥0} ]: for any indicator function χ or more generally for any χ ∈ L ∞ (R N × [0, T ]) with values in [0, 1], the Hamiltonian H[χ] depends on χ in a nonlocal way; typically in our examples, it is obtained by a convolution procedure between χ and a physical kernel (either only in space or in space and time). In particular, H[χ] is continuous in space but has no particular regularity in time. However, the H[χ] equation is always well posed. More precisely, we assume that for any χ ∈ L ∞ (R N × [0, T ]; [0, 1]) with bounded support, H[χ](x, t, p, A) defines a measurable function of (x, t, p, A) ∈ R N × [0, T ] ×