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The reduced capture history (RCH), compiled from complete capture histories of uniquely marked animals, for a given pooling interval contains the same information as would be obtained from experiments where (i) a single sample lasts the duration of the pooling interval; (ii) an identical batch mark is applied to animals captured in a series of samples carried out during the pooling interval. For stationary populations, biases are calculated for the RCH estimates for all parameters in the Jolly-Seber (J-S) model. The results are verified using simulation. The biases are functions of the survival and capture probabilities and the degree of pooling; they are less than 5% for the total population, birth and survival rates, and probability of capture during the pooling interval if the mortality and capture probabilities do not exceed about 50% per pooling interval. The marked population, marked fraction, and probability of recapture cannot estimated directly by the RCH method but can be obtained iteratively from the bias formulae. The biases in other parameters can be reduced by the same procedure. Alternative estimates are derived that are not detectably biased, for any estimate, for mortality and capture probability up to about 60% per pooling period. The new estimates have higher sample variances than the RCH estimates, but for large populations with high mortalities and capture probabilities the difference is small.