  We establish the existence of semi-wavefronts solutions for a non-local
delayed reaction-diffusion equation with monostable nonlinearity. The existence
result is proved for all speeds $c\geq c_\star$, where the determination of
$c_\star$ is similar to the calculation of the minimal speed of propagation.
The results are applied to some non-local reaction-diffusion epidemic and
population models with distributed time delay.
