For the integrate-and-fire model with or without reversal potentials, we consider how correlated inputs affect the variability of cellular output. For both models, the variability of efferent spike trains measured by coefficient of variation (CV) of the interspike interval is a nondecreasing function of input correlation. When the correlation coefficient is greater than 0.09, the CV of the integrate-and-fire model without reversal potentials is always above 0.5, no matter how strong the inhibitory inputs. When the correlation coefficient is greater than 0.05, CV for the integrate- and-fire model with reversal potentials is always above 0.5, independent of the strength of the inhibitory inputs. Under a given condition on correlation coefficients, we find that correlated Poisson processes can be decomposed into independent Poisson processes. We also develop a novel method to estimate the distribution density of the first passage time of the integrate-and-fire model.