Eleven 1-pool, seven 2-pool, and three 3-pool models were compared in fitting gas production data and predicting in vivo NDF digestibility and effective first-order digestion rate of potentially digestible NDF (pdNDF). Isolated NDF from 15 grass silages harvested at different stages of maturity was incubated in triplicate in rumen fluid-buffer solution for 72 h to estimate the digestion kinetics from cumulative gas production profiles. In vivo digestibility was estimated by the total fecal collection method in sheep fed at a maintenance level of feeding. The concentration of pdNDF was estimated by a 12-d in situ incubation. The parameter values from gas production profiles and pdNDF were used in a 2-compartment rumen model to predict pdNDF digestibility using 50 h of rumen residence time distributed in a ratio of 0.4:0.6 between the non-escapable and escapable pools. The effective first-order digestion rate was computed both from observed in vivo and model-predicted pdNDF digestibility assuming the passage kinetic model described above. There were marked differences between the models in fitting the gas production data. The fit improved with increasing number of pools, suggesting that silage pdNDF is not a homogenous substrate. Generally, the models predicted in vivo NDF digestibility and digestion rate accurately. However, a good fit of gas production data was not necessarily translated into improved predictions of the in vivo data. The models overestimating the asymptotic gas volumes tended to underestimate the in vivo digestibility. Investigating the time-related residuals during the later phases of fermentation is important when the data are used to estimate the first-order digestion rate of pdNDF. Relatively simple models such as the France model or even a single exponential model with discrete lag period satisfied the minimum criteria for a good model. Further, the comparison of feedstuffs on the basis of parameter values is more unequivocal than in the case of multiple-pool models.