We assess, both numerically and theoretically, how positively correlated Poisson inputs affect the output of the integrate-and-fire and Hodgkin-Huxley models. For the integrate-and-fire model the variability of efferent spike trains is an increasing function of input correlation, and of the ratio between inhibitory and excitatory inputs. Interestingly for the Hodgkin-Huxley model the variabilit...