  A general theoretical approach based on the results of statistical optics is
used for the analysis of the transverse coherence properties of 3-rd generation
synchrotron sources and x-ray free-electron lasers (XFEL). Correlation
properties of the wavefields are calculated at different distances from an
equivalent Gaussian Schell-model source. This model is used to describe
coherence properties of the five meter undulator source at the synchrotron
storage ring PETRA III. In the case of XFEL sources the decomposition of the
statistical fields into a sum of independently propagating transverse modes is
used for the analysis of the coherence properties of these new sources. A
detailed calculation is performed for the parameters of the SASE1 undulator at
the European XFEL. It is demonstrated that only a few modes contribute
significantly to the total radiation field of that source.
