The effects of supplements containing different rumen-undegradab le protein (RUP) levels on the ruminal passagerate of particles and liquid of steers grazing Brachiaria brizantha were evaluated in this study. Samples were collected in two seasons of the year (season 1 - May, June and July/2000 and season 2 - March, April and May/2001). In season 1, animals were housed in individual stalls and were fed supplements containing 20, 40 or 60% RUP plus Brachiaria brizantha hay and had free access to a mineral mix. In season 2, steers were distributed to one of three treatments as follows: T₀ = Brachiaria brizantha pasture + ad libitum mineral mix, T₄₀ = pasture + 40% RUP supplement, or T₆₀ = pasture + 60% RUP supplement. Chromium mordant was used to estimate ruminal passage rate of particles; fluid passage rate was estimated using CoEDTA during three periods from August to September/2001 using the same animals of season 2. Estimation of the kinetic parameters of ruminal passage of particles was obtained by adjusting data to different bicompartimental models (G1G1, G2G1, G3G1, G4G1, G5G1 e G6G1) while the model G1G1 was used to estimate the kinetic parameters of ruminal passage of liquid. The criteria to choose the best model were the observed frequency of minimum values for the mean residual square obtained with the adjustment of different models and the number of signal runs of standardizedresidues. The models G2G1 e G3G1 were the most efficientto estimate the kinetic parameters of ruminal passage of particles in seasons 1 and 2, respectively. Different supplement RUP levels did not affect the estimation of mean ruminal retention time of both particles and liquid.