We investigated the late-time (asymptotic) behavior of tracer test breakthrough curves (BTCs) with rate-limited mass transfer (e.g., in dual-porosity or multiporosity systems) and found that the late-time concentration c is given by the simple expression c=tad{c0g-0(∂g/∂t)>}, for t≫tad and t&agr;≫tad, where tad is the advection time, c0 is the initial concentration in the medium, m0 is the zeroth moment of the injection pulse, and t&agr; is the mean residence time in the immobile domain (i.e., the characteristic mass transfer time). The function g is proportional to the residence time distribution in the immobile domain; we tabulate g for many geometries, including several distributed (multirate) models of mass transfer. Using this expression, we examine the behavior of late-time concentration for a number of mass transfer models. One key result is that if rate-limited mass transfer causes the BTC to behave as a power law at late time (i.e., c~t-k), then the underlying density function of rate coefficients must also be a power law with the form &agr;k-3 as &agr;→0. This is true for both density functions of first-order and diffusion rate coefficients. BTCs with k<3 persisting to the end of the experiment indicate a mean residence time longer than the experiment, and possibly an infinite residence time, and also suggest an effective rate coefficient that is either undefined or changes as a function of observation time. We apply our analysis to breakthrough curves from single-well injection-withdrawal tests at the Waste Isolation Pilot Plant, New Mexico. ¿ 2000 American Geophysical Union