  We study the large time asymptotic behavior of the solutions of the linear
parabolic equation with delay $(*)$: $u_{t}(t,x) = u_{xx}(t,x) - u(t,x) +
\int_{\mathbb{R}} k(x-y) \, u (t-h, y)\, dy$, $x \in \R$, $\ t >0$, and $k(x)
\in L^1(\R)$. As an application we get estimates on the measure of level sets
of non local KPP type equations with delay. For this type of nonlinear
equations we prove that, in contrast with the classical case, the solution to
the initial value problem with data of compact support may not be persistent.
