AbstractDiffusion in complex heterogeneous structures, for example, the neural fiber system, is non‐gaussian. Recently, several methods have been introduced to address the issue of non‐gaussian diffusion in multifiber systems. Some are based on apparent diffusion coefficient (ADC) analysis; and some are based onq‐space analysis. Here, using a simple mathematic derivation, ADC‐based models are shown to be mathematically self‐inconsistent in the presence of non‐gaussian diffusion. Monte Carlo simulation on restricted diffusion is applied to demonstrate the poor data fitting that can result from ADC‐based models. Specific comparisons are performed between two generalized diffusion tensor imaging methods: one of them is based on ADC analysis, and the other is shown to be consistent withq‐space formalism. The issue of imaging asymmetric microstructures is also investigated. Signal phase and spin exchange are necessary to resolve multiple orientations of an asymmetric structure. Magn Reson Med 54:419–428, 2005. © 2005 Wiley‐Liss, Inc.