  We propose an extension to multivariate time series of the phase-randomized
Fourier-transform algorithm for generating surrogate data. Such surrogate data
sets must mimic not only the autocorrelations of each of the variables in the
original data set, they must mimic the cross-correlations {\em between} all the
variables as well. The method is applied both to a simulated example (the three
components of the Lorenz equations) and to data from a multichannel
electroencephalogram.
