Fecal profiles (n) of the particulate markers Cr (n = 52) and La (n = 30) and the fluid marker complex Co-EDTA (n = 57) were obtained from digestion kinetic studies with cows, steers, and sheep with the aim of evaluating mathematical models designed to interpret marker excretion profiles in feces. The models evaluated were the multicompartmental model of Dhanoa et al. (1985), the Gamma model described as GN by Pond et al. (1988), and the GNG1 model proposed by Matis (1972). Models were fitted by ordinary nonlinear least squares and evaluated on the basis of the Akaike information criterion and derived measures (information-likelihood criteria). Despite remarkable differences in terms of information-likelihood measures, the models were quite similar in terms of visual adherence to observed time profiles and presented overlapping interval estimates for compartment mean retention times. The major relative numerical discrepancies observed among the models were related to the mean and variance of the transit time for the first appearance of the marker in feces. The model with the best performance in mimicking the marker profiles was the GN model; the GNG1 model and the multicompartmental model were almost equivalent in terms of information-likelihood. Therefore, we derived a mathematical model to account for digestibility (D) and fill (Q) of the ruminoreticular digesta whenever the best model used to interpret marker studies, chosen based on information-likelihood criteria, was the GN model. Therefore, the GN model solutions for D and Q are as follows: D = [k/(λ + k)] Σ_i[λ/(λ + k)]^i–1, and Q = AF/(λ + k) Σ_i[λ/(λ + k)]^i–1 + UFN/λ, for i = 1, 2, …, N. In the models, k, λ, A, and U are the fractional rate of the pool of escapable particles in the rumen, the fractional escape of particles from the rumination pool to the escapable pool, the fiber fraction available for digestion, and the unavailable fiber fraction, respectively. F is the average daily intake rate, and N is the order of time dependency. Funded by CNPq, CAPES, and FAPERJ.