Comportentment Asymptotique des Systems Doublement Orthogonaux de Berman: Une Approche Elementaire Ahmed Zeriahi Abstract      Given a domain $D \in X$ in a complex analytic space $X$ and a nonpluripolar compact set $K \in D$, it is possible to construct in a natural way two Hilbert spacec $H_1$ and $H_2$ of Bergman type attached to the “condenser” $(K,D)$ in the sense that the following inclusions $H_1 \hookrightarrow \mathcal O(D) \hookrightarrow \mathcal O(K) \hookrightarrow H_0$ are continous. Then generalizing  a classical construction due to Bergman. It is possible to construct a dobly orthogonal system in $H_1$ and $H_0$. Our main goal here is to describe, in a completely elementary way, the asymptoticl behaviour of this doubly orthogonal system in terms of the {\em plurisubharmonic measure} of the  condenser $(K,D)$, using classical ideas of Bergman as well as classical results from both Pluripotential Theory and Spectral Theory.