  We consider a Fisher-KPP-type equation, where both diffusion and nonlinear
part are nonlocal, with anisotropic probability kernels. Under minimal
conditions on the coefficients, we prove existence, uniqueness, and uniform
space-time boundedness of the positive solution. We investigate existence,
uniqueness, and asymptotic behavior of monotone traveling waves for the
equation. We also describe the existence and main properties of the front of
propagation.
