  This paper deals with the stability of semi-wavefronts to the following delay
non-local monostable equation: $\dot{v}(t,x) = \Delta v(t,x) - v(t,x) +
\int_{\R^d}K(y)g(v(t-h,x-y))dy, x \in \R^d,\ t >0;$ where $h>0$ and $d\in\Z_+$.
We give two general results for $d\geq1$: on the global stability of
semi-wavefronts in $L^p$-spaces with unbounded weights and the local stability
of planar wavefronts in $L^p$-spaces with bounded weights. We also give a
global stability result for $d=1$ which includes the global stability on
Sobolev spaces. Here $g$ is not assumed to be monotone and the kernel $K$ is
not assumed to be symmetric, therefore non-monotone semi-wavefronts and {\it
backward traveling fronts} appear for which we show their stability. In
particular, the global stability of critical wavefronts is stated.
