An explicit model is used to obtain estimation equations for 6 key parameters of the maternal-fetal system: the steady state hormone secretion (or appearance) rates into maternal and fetal circulations, SRM and SRF; maternal-tofetal and fetal-to-maternal hormone transfer rates, QMF and QFM and the maternal and fetal irreversible hormone disposal rates, QMO and QFO Each estimator is given in terms of data from a dual tracer in utero experiment, which can be performed with either brief injection or constant infusion techniques. Complementary analytic and computer simulation techniques for error analysis are also developed to assess the reliability of numerical estimates determined from these equations. These techniques are applied to data previously reported for cortisol and calcium in the maternal-fetal systems of the sheep and monkey, respectively. For cortisol, the estimates SRM = 46.3 and SRF = 1.07 μg/min confirm those previously reported; and coefficients of variation for both are approximately 11%. Estimates (and coefficients of variation) previously unreported for cortisol are: QMF = 0.44 (13%), QFM = 0.82 (13%), QMO = 46.7 (11%) and QFO = 0.69 (19%) Mg/min. For calcium, estimates are: SRM = 1112 (10%), SRF = 96 (40%), QMF = 363 (13%), QFM = 254 (13%), QMO = 1003 (10%) and QF0 = 205 (17%) mg/day, assuming coefficients of variation of 5% in the experimental data; QMF and QFM were previously reported to be 118 and 334 mg/day. Analysis of 3 additional simulated experiments illustrates that, in certain cases, highly unreliable or useless parameter estimates can be obtained from very reliable experimental data. These situations, which cannot be detected without error analysis, are analyzed by specific Monte Carlo simulation methods. (Endocrinology93: 324, 1973)