Spike-timing variability has a large effect on neural information processing. However, for many systems little is known about the noise sources causing the spike-response variability. Here we investigate potential sources of spike-response variability in auditory receptor neurons of locusts, a classic insect model system. At low spike frequencies, our data show negative interspike-interval correlations and interspike-interval distributions that match the inverse Gaussian distribution. These findings can be explained by a white-noise source that interacts with an adaptation current. At higher spike frequencies, more strongly peaked distributions and positive interspike-interval correlations appear, as expected from a canonical model of supra-threshold firing driven by temporally correlated (i.e. colored) noise. Simulations of a minimal conductance-based model of the auditory receptor neuron with stochastic ion channels exclude the delayed rectifier as a possible noise source. Our analysis suggests channel noise from an adaptation current and the receptor or sodium current as main sources for the colored and white noise, respectively. By comparing the interspike-interval statistics with generic models, we find strong evidence for two distinct noise sources. Our approach does not involve any dendritic or somatic recordings that may harm the delicate workings of many sensory systems. It could be applied to various other types of neurons, in which channel noise dominates the fluctuations that shape the neuron's spike statistics.