Large-scale inhomogeneities in natural porous media profoundly affect the dynamic response of conveyed tracers. It isproposed that tracer dynamics in heterogeneous porous media can be represented by temporal moments based on parallel and series unit models of homogeneous columns, stirred volumes, or mass-transfer-connected closed compartments. The rules of combining the moments for elementaty volumes are based on units (1) in series, where output from the preceding units is the input to the succeeding unit, and (2) in parallel, where the splitting or joining flow paths control the response. For a network of elementary volumes in series or parallel, fate and transport of contaminants in heterogeneous media can be analyzed simply in a deterministic framework. Results for several simple series and parallel models show the wealth of responses that can be quantitatively described by this procedure.