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There is growing evidence that water seepage in thick unsaturated zones in fractured rocks may occur in non-volume-averaged fashion, as relatively ’slow’ flow in the rock matrix, and ’fast’ flow along localized preferential pathways in fractures. This poses difficult challenges for mathematical modeling. We summarize recent field observations of subsurface flow and transport from semi-arid regions, discuss alternative approaches for modeling fast preferential flow, and evaluate prospects for resolving current uncertainties. It is concluded that modeling of flow in fractured unsaturated zones is complex, but feasible, while modeling of transport processes is more difficult and less certain. We emphasize that successful modeling requires clear and specific objectives, but does not necessarily require a complete and detailed understanding of all processes and properties of a system. In order to achieve a robust modeling capability, as needed for engineering assessment and design of waste containment systems, it is suggested that two or more alternative modeling approaches be developed simultaneously for a given site. (C) 1999 Elsevier Science B.V. All rights reserved.