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We derive a dynamical equation for the spike emission rate 驴 (t) of a homogeneous population of Integrate-and-Fire (IF) neurons, in an "extended" mean-field approximation (i.e., taking into account both the mean and the variance of the afferent current). Conditions for stability and characteristic times of the population transient response are investigated, and both are shown to be naturally expressed in terms of single neuron current-to-rate transfer function. Finite-size effects are incorporated by a stochastic extension of the mean-field equations and the associated Fokker-Planck formalism, and their implications for the frequency response of the population activity is illustrated through the power spectral density of v(t). The role of synaptic delays in spike transmission is studied for an arbitrary distribution of delays.