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 cross-correlation function is discussed. We also discuss how these nonlinear phenomena affect noise filtering and tissue characterization using statistical parameters.