Fields generated in a large number of nonlinear-optical processes (including those with losses) have a Wigner distribution that is Gaussian centered around the mean value of the field. We show that the Bell inequality for an optical-correlation experiment with two coupled modes generated in a nonlinear process can be expressed as an inequality relating to the parameters of the underlying Wigner distribution function. We consider examples of parametric down-conversion and a two-mode squeezed laser, which can be used in experiments to demonstrate quantum nonlocality. © 1991 The American Physical Society.