  We consider the problem governed by the gradient ODE $x'=\nabla F(x)$ in
$\mathbb{R}^d$ on which we assume that it has a finite number of hyperbolic
equilibria whose stable and unstable manifolds intersect transversally. This
problem is perturbed by the memory term $x'(t)=\nabla
F(x(t))+\varepsilon\int_{-\infty}^t M(t-s)x(s)\, ds$ where $\varepsilon>0$ is a
small constant. The key result is that the structure of connections between the
equlibria of the unperturbed problem is exactly preserved for a small
$\varepsilon>0$.
