with small holes or inclusions shrinking to points. This type of problems is of interest not only for the mathematical aspects but also in view of concrete applications to the investigation of physical models in fluid dynamics, in elasticity, and in thermodynamics. For example, problems on domains with small holes or inclusions can arise in the modeling of dilute composites or of perforated elastic bodies. In this paper, we will focus on a mixed problem for the Laplace operator in a bounded domain with two moderately close small holes. In other words, we will consider a domain with two cavities such that both their size and the distance between them tend to zero. However, we will assume that the perforations are ‘moderately close’, *i.e.*, the distance tends to zero ‘not faster’ than the size.

In order to introduce the problem, we first define the geometric setting. We fix once for all a natural number $$n\in {\mathbb{N}}\setminus\{0,1 \}\, .$$ Then we consider $\alpha\in]0,1[$ and three subsets $\Omega^i_1$, $\Omega^i_2$, $\Omega^o$ of ${\mathbb{R}}^{n}$ satisfying the following assumption: $$\label{dom}
\begin{split}
&\text{$\Omega^i_1$, $\Omega^i_2$,  $\Omega^o$ are bounded open connected subsets of ${\mathbb{R}}^{n}$}\\
&\text{of class $C^{1,\alpha}$ such that ${\mathbb{R}}^{n}\setminus{\mathrm{cl}}\Omega^i_1$, ${\mathbb{R}}^{n}\setminus{\mathrm{cl}}\Omega^i_2$ and ${\mathbb{R}}^{n}\setminus{\mathrm{cl}}\Omega^o$ are}\\
&\text{connected  and  that $0\in 