We have analysed EXOSAT ME X-ray light curves of a sample of AGN assum
ing a stochastic process in these sources. The result is a significant
anti-correlation between the relaxation timescale tau, derived from t
his stochastic model fit, and the photon index Gamma of the X-ray spec
trum. This establishes for the first time a relationship between varia
bility properties and spectral properties of the emitted X-ray flux of
AGN. Even though the physical mechanism for the variations is far fro
m dear, models employing the stochastic superposition of discrete even
ts appear most promising. We propose Comptonization as a possible caus
e for the relationship.