The variance of the image noise in computed X-ray transmission tomography (CT) due to quantum noise is in a first approximation a nonlinear function of X-ray attenuation. Beam hardening in CT is also a nonlinear function of attenuation. We present a theoretical study of both phenomena. Computer simulations and numerical results show that both nonlinear dependencies have quite similar effects on image quality. We also show how the two-dimensional distribution of the noise variance in a CT image is a weighted superposition of images obtained by backprojecting integer powers of the noiseless projection data corresponding to the scanned object. The streak-like pattern in the image noise due to the anisotropic nature of the noise crosscorrelation function is discussed. We also discuss how these nonlinear phenomena affect noise filtering and tissue characterization using statistical parameters. © 1979 Raven Press, New York.