A nonrandom and unknown signals(t), in additive Gaussian noise with mean zero and known covariance function, is passed through a known memoryless nonlinearityf(x). The identification of the signal from the distributions or moments of the output process is considered. Arbitrary signals can be identified for monotonic and for certain odd, not necessarily monotonic, nonlinearities; these include hard limiters, quantizers, and infinite-interval windows. Arbitrary signals can be identified up to a global sign for two distinct classes of even nonlinearities; these include full-wave even\nuth-law devices and symmetric-interval windows.