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We present results of computer studies of the spatial correlations in two nonequilibrium model systems. These are lattice gases on 2 ' described by (apparently) non-Gibbsian probability measures which are stationary with respect to simple, anisotropic, particleconserving stochastic dynamics. The translation-invariant pair correlation functions G(r) are found to decay like a quadrupole field, i.e. for r = (2, U), G(r) -(ax2 -by2)/r4, over a range of parameter values corresponding to <> in the dynamics. This gives the strongest evidence to date of the generic nature of long-range correlations in conservative anisotropic nonequilibrium systems-in accord with some recent theoretical predictions. Some other properties of these models are also calculated. In particular it is found that, despite the slow decay of the correlations, the fluctuations in particle number look Gaussian.

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