In terms of mathematical structure, the voltage-conductance kinetic systems for neural networks can be compared to a kinetic equations with a macroscopic limit which turns out to be the Integrate and Fire equation. This article is devoted to mathematical study 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 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 kinetic equation shares some similar dynamics.