This paper presents a computer algorithm that is capable of cogenerating pairs of three-dimensional, cross-correlated random fields. The algorithm produces random fields of real variables by the inverse Fourier transform of a randomized, discrete three-dimensional spectral representations of the variables. The randomization is done in the spectral domain in a way that preserves the direct power and cross-spectral density structure. Two types of cross spectra were examined. One type specifies a linear relationship between the two fields, which produces the same correlation scales for both variables but different variances. The second cross spectrum is obtained from a specified transfer function and the two power spectra, and it produces fields with different correlation scales. For both models the degree of correlation is specified by the coherency. A delay vector can also be specified to produce an out-of-phase correlation between the two fields. The algorithm is very efficient computationally, is relatively easy to use, and does not produce the lineation problems that can be encountered with the turning bands method. Perhaps most important, this random field generator is capable of co-generating cross-correlated random fields. ¿ American Geophysical Union 1993