This paper deals with the existence of traveling fronts for the reaction-diffusion equation: ∂u ∂t −∆u = h(u, y) t ∈ R, x = (x1, y) ∈ R . We first consider the case h(u, y) = f(u) − αg(y)u where f is of KPP or bistable type and lim|y|→+∞ g(y) = +∞. This equation comes from a model in population dynamics in which there is spatial spreading as well as genetic mutation of a quantitative genetic tr...