Fecal concentrations of chromium and cobalt, following a single labeling dose of Cr-mordanted fiber and Co-EDTA to the rumen, were obtained from two experiments: one with beef cows fed two diets before and after parturition, and one with growing bull calves fed two diets of high and low fill volume. These data were used to compare three optional models that estimated the whole digestive tract kinetics of particles and solutes and fecal output, with a fourth model that estimated particle kinetics only. The first model (M1) assumes separate routes for particles and solutes, with two bypass fluxes (i.e., simultaneous fluxes from one pool to more than one other pool) in the particle route and one in the solute route. The second model (M2) is similar to M1, but allowance is made for some of the particles to pass to the solute route. The third model (M3) assumes that most of the kinetic variables in the solute route are identical to the correspondent variables in the particle route. The fourth model (M4) assumes an unspecified number of sequential compartments with constant increase of the outflow rate from each compartment to the next one, without allowance for any bypass fluxes. All the models could fit all the data sets. Goodness of fit was the best with M2 and the worst with M3. Goodness of fit of the particle curve with M2 was comparable to that of M4. Model M1 estimated the shortest and M3 estimated the longest total retention time (TRT) for particles (72.8, 85.0, and 91.2 h for M1, M2, and M3, respectively), and the partition of retention time between the different pools differed among models. There were no significant differences among models in their estimates of solute TRT (30.2, 31.5, and 30.8 h for M1, M2, and M3, respectively). Fecal output estimations were similar among models, all of them overestimating the predetermined measurements by 9.5 to 13%. The r2 of the linear regression of the estimated on the determined fecal output was .74, .75, and .70 for M1, M2, and M3, respectively.