The objective of this investigation is to analyse the impact of differential mortality by birth order and age of the mother on the indirect estimates of child mortality. This indirect method was proposed by professor W. Brass and is based on reports about the number of children ever born and children surviving to women classified by age groups. The first step was to relax the constraints imposed on the method by the assumption that the risk of dying is invariant with birth order, mother's age and birth spacing patterns. To that effect, on the basis of the available evidence, a functional description of mortality by age of the child, which takes into account these differentials, was proposed. Then a beta-binomial probability distribution was used for describing fertility patterns by marriage duration and birth order, and a negative binomial distribution was adopted for describing nuptiality patterns. The models were tested using data from different countries and the results were satisfactory. All the necessary calculations to simulate proportions of children surviving (or dead) by age of the mother and number of children ever born were then executed on the basis of these three demographic models. Birth distributions by age of the mother and birth order were obtained by compounding the fertility model by marriage duration with the nuptiality model. Then, under certain assumptions, mean time-exposures to the risk of dying were calculated for children by birth order, current age of the mother, and parity. These exposures were combined with the functional description of mortality mentioned above, to yield proportions of children surviving by age and parity of the mothers. Adjusting factors by mother's age groups were calculated by relating these results to those obtained when mortality is assumed to be a function of the child's age only. These factors make estimates of mortality levels, obtained from reports from the younger mothers, comparable to the overall mortality for all children. They were applied to data from Peru and the results appeared to be very reasonable. An important conclusion from the analysis of the average exposures to risk for children by mother's age and parity is that the exposures are fairly constant by family size, while the variation in the proportions of children surviving is significant. The practical implication of these findings is that variations in the proportions of children surviving are basically caused by differential mortality. The application of the technique was illustrated with two practical examples. Proportions of children surviving by family size and age of the mother from Bolivia, 1976 Census, and from Guatemala, 1970 Census, were analysed. An enormous differential in mortality by family size was observed in both countries. The patterns of the relative risks by family size were very similar in both countries.