For a positive PRC (type I), the SCC is always negative at lag 1. At higher lags, we find either a monotonically decaying (Fig.1A) or oscillating (Fig.1C) behavior of the SCC depending on the strength of adaptation. Similar correlation structures have been observed in different experimental studies (see e.g. [2]). Despite the distinct patterns, the total correlation as expressed by the sum of the SCC over all lags displays a universal value close to -0.5 at high firing rates and strong adaptation. As an example of a type I neuron, we discuss one-dimensional integrate-and-fire (IF) neurons with adaptation (like e.g. the adaptive exponential IF model [3]) operating in the supra-threshold regime. For these models, the different behaviors of the SCC can be explained by qualitatively different structures of the phase plane spanned by the voltage and the adaptation variables. Our theory also predicts that adapting neurons with a partly negative PRC (type II phase resetting) can additionally exhibit non-negative ISI correlations, which is indeed found in a two-dimensional IF model with adaptation (Fig.1D,E). Thus, adapting neurons can show a richer repertoire of correlation patterns than previously thought.