Polychromatic stationary propagation-invariant fields with complete spatial coherence in the space-frequency domain are considered. In general, the field is shown to be spatially partially coherent in the space-time domain, apart from transversely achromatic fields with complete transverse coherence. Particular attention is paid to fields that possess the same cone angle at each frequency; these are stationary counterparts of pulsed conical fields known as X waves. It is shown that, for such fields, the radius of the space-time-domain transverse coherence area depends critically on the bandwidth of the power spectrum and can be comparable to the central-lobe radius of the monochromatic field component at the peak frequency of the spectrum.
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