Data on ovulation rate and numbers of ova and transferable embryos recovered from superovulated cattle and sheep were analysed using generalized linear models, quasi-likelihood, restricted maximum likelihood (reml) and generalized linear mixed models (glmms). The data pertained to the operation of nucleus breeding schemes in cattle and the commercial application of embryo transfer in sheep. Results of the analyses showed that generalized linear models involving Poisson and Binomial distributions were inappropriate because of over-dispersion, and that analyses using quasi-likelihood to model negative binomial and P-binomial distributions were more suitable. Factors identified as important in determining the results in cattle were the number of previous superovulations (a higher proportion of transferable embryos were obtained in the initial flush compared to subsequent recoveries in two out of three sets of data), the donor (significant in all analyses with repeated recoveries) and its mate (significant in some analyses). In sheep, the use of pFSH or hMG for superovulation increased embryo yields above those obtained with PMSG + GnRH. Analyses of a further data set for sheep showed the effect of breed was ambiguous. The effects of donors and their mates were treated as random effects in analyses involving reml and glmms. Results showed that the repeatability of the number of transferable embryos produced per donor ranged between 0.13 and 0.23 in three sets of data and was significant in all cases. In these analyses the variance among mates was not significantly different from zero. The results of analyses were used to develop a random generator to simulate the numbers of ova and embryos recovered from a cow following superovulation. By sampling from negative binomial distributions where the scale factor used for each cow was a normally distributed deviate, distributions were obtained which had the same mean, variance and repeatability as those observed.