The voltage-conductance systems for neural networks has been introduced by late D. Cai and his co-authors. In terms of mathematical structure, it can be compared to a kinetic equations with a macroscopic limit which turns out to be the Integrate and Fire equation. This talk is devoted to a mathematical description of the slow-fast limit of the kinetic type equation to an I&F equation. After proving the weak convergence of the voltage-conductance kinetic problem to potential only I&F equation, we prove strong a priori bounds and we study the main qualitative properties of the solution of the I&F model, with respect to the strength of interconnections of the network. In particular, we obtain asymptotic convergence to a unique stationary state for weak connectivity regimes. For intermediate connectivities, we prove linear instability and numerically exhibit periodic solutions. These results about the I&F model suggest that the more complex voltage-conductance kinetic equation shares some similar dynamics in the correct range of connectivity.