Mating and calving records for 51,084first-parity heifers in Australian Angus herds wereused to examine the relationship between probabilityof calving to first insemination (CFI) in artificial inseminationand natural service (NS) mating data. Calvingto first insemination was defined as a binary trait forboth sources of data. Two Bayesian models were employed:1) a bivariate threshold model with CFI in AIdata regarded as a trait separate from CFI in NS dataand 2) a univariate threshold model with CFI regardedas the same trait for both sources of data. Posteriormeans (SD) of additive variance in the bivariate analysiswere similar: 0.049 (0.013) and 0.075 (0.021) forCFI in AI and NS data, respectively, indicating lack ofheterogeneity for this parameter. A similar trend wasobserved for heritability in the bivariate analysis, withposterior means (SD) of 0.025 (0.007) and 0.048 (0.012)for AI and NS data, respectively. The posterior means(SD) of the additive covariance and corresponding geneticcorrelation between the traits were 0.048 (0.006)and 0.821 (0.138), respectively. Differences were observedbetween posterior means for herd-year variance:0.843 vs. 0.280 for AI and NS data, respectively, whichmay reflect the higher incidence of 100% conceptionrates within a herd-year class (extreme category problem)in AI data. Parameter estimates under the univariatemodel were close to the weighted average of thecorresponding parameters under the bivariate model.Posterior means (SD) for additive, herd-year, and servicesire variance and heritability under the univariatemodel were 0.063 (0.007), 0.56 (0.029), 0.131 (0.013),and 0.036 (0.007), respectively. These results indicatethat, genetically, cows with a higher probability of CFIwhen mated using AI also have a high probability ofCFI when mated via NS. The high correlation betweenthe two traits, along with the lack of heterogeneity forthe additive variance, implies that a common additivevariance could be used for AI and NS data. A single-traitanalysis of CFI with heterogeneous variances forherd-year and service sire could be implemented. Thelow estimates of heritability indicate that response toselection for probability of calving to first inseminationwould be expected to be low.