In French dairy goats, 825 bucks (471 Alpine and 354 Saanen) were genotyped with the Illumina goat SNP50 Bead-Chip. Previous studies have shown that (i) using a two-step approach applied to a genomic best linear unbiased prediction (GBLUP) did not lead accuracies of the genomic estimated breeding values (GEBV) to the level of the ones of the parent average breeding values for young candidates; (ii) differences between Alpine and Saanen breed in genetic structure make the interest of multi-breed genomic evaluation questionable. The objective of this study was to compare in a GBLUP single step approach three models: 1) a multi-breed model with Saanen and Alpine considered as the same breed and using the same genetic parameters, 2) a within-breed model analysed separately for each breed, and 3) a multiple trait one with genetic correlation (estimated, equal to 0 or equal to 0.99) between Alpine and Saanen. Five milk production traits, somatic cell scores (SCS) and five udder type traits were analysed. Quality of predictions was evaluated by cross validation looking at Pearson correlations between GEBV and daughter yield deviations (DYD, i.e their pseudo-performances) for 252 validation males. Accuracies of GEBV or “model accuracies” were estimated from prediction error variances and derived for the148 youngest candidates (genotyped but no phenotyped). Pearson correlations between GEBV and DYD estimated for validation males ranged from 0.35 for milk yield in Alpine breed using the multi-breed model to 0.73 for protein content in Saanen breed using the within-breed model. Using the single step approach instead of the two-step one increased the Pearson correlations for all traits by 10% for milk yield to 60% for udder floor position. The prediction accuracies achieved with the multiple trait models were similar to the ones obtained with multi-breed or multiple trait models whatever the genetic covariance levels considered. They were higher in Saanen breed than in Alpine breed due to higher relationship level between training and testing sets in Saanen breed. The average model accuracies estimated on the 148 candidates bucks ranged from 0.62 for SCS to 0.74 for protein content, both in Saanen breed. Model accuracies were higher in Saanen breed than in Alpine breed except for SCS. The three different models led to no differences in average model accuracies for candidates. These model accuracies were higher than the accuracy of candidates’ parent average breeding values for all traits. Using single step approaches instead of two-step ones increased model accuracy from 28% for udder type traits and SCS to 37% for milk and fat yields.