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We discuss in detail the broad band X-ray variability expected in Seyfertgalaxies in the framework of a Compton cooled corona model. Variations in theoptical depth tau of the corona cause spectral changes in the Comptonizedemission in the sense that the spectrum steepens and the temperature decreaseswith increasing tau. If the corona is pair dominated, tau is determined by thecompactness (proportional to luminosity for fixed size). This yields a definiterelation between spectral shape and intensity implying a variation in intensityof a factor 10 for a change of 0.2 in the 2-10 keV spectral index. For low pairdensity coronae, no definite prediction is possible. In the absence ofsubstantial changes in the structure of the corona, the soft thermal componentcorrelates with the medium-hard Comptonized component. Examples are computedusing the ROSAT response matrix, showing that current observations of NGC 5548and Mrk 766 showing different behaviours can be reconciled with the model. Thespectral behaviour of Mrk 766 strongly suggests that the coronal plasma in thissource is not pair dominated.

X‐Ray Variability and Correlations in the Two‐Phase Disk‐Corona Model for Seyfert Galaxies