  We investigate a Dirichlet problem for the Laplace equation in a domain of
$\mathbb{R}^2$ with two small close holes. The domain is obtained by making in
a bounded open set two perforations at distance $|\epsilon_1|$ one from the
other and each one of size $|\epsilon_1\epsilon_2|$. In such a domain, we
introduce a Dirichlet problem and we denote by $u_{\epsilon_1,\epsilon_2}$ its
solution. We show that the dependence of $u_{\epsilon_1,\epsilon_2}$ upon
$(\epsilon_1,\epsilon_2)$ can be described in terms of real analytic maps of
the pair $(\epsilon_1,\epsilon_2)$ defined in an open neighborhood of $(0,0)$
and of logarithmic functions of $\epsilon_1$ and $\epsilon_2$. Then we study
the asymptotic behaviour of of $u_{\epsilon_1,\epsilon_2}$ as $\epsilon_1$ and
$\epsilon_2$ tend to zero. We show that the first two terms of an asymptotic
approximation can be computed only if we introduce a suitable relation between
$\epsilon_1$ and $\epsilon_2$.
