The Guzerá breed is an important Brazilian genetic resource and has been widely used as a pure breed and in crossbreeding strategies to produce animals adapted to tropical climatic conditions. In the last 30 years, some breeders have included selection for dairy traits in addition to selection for beef traits to obtain economic benefits from the sale of meat and milk in dual-purpose production systems. Dual-purpose studies in Guzerá cattle are recent and a previous study showed that there is no genetic antagonism between milk production, growth traits, and age at first calving in these animals, allowing joint selection for these traits. Given the advantages of including marker information such as single nucleotide polymorphisms (SNP) in genetic evaluations, efforts were also made to genotype Guzera animals, particularly those selected for milk and dual-purpose. In this sense, the overall objective of this thesis was to perform genetic and genomic evaluations considering the most important traits selected in Guzerá cattle for both dairy and beef in Guzerá cattle. First, the variance components and genetic parameters for the traits were estimated using bi-trait models. The genetic and phenotypic correlations were all favorable. The absence of genetic antagonism between the reproductive, beef and milk traits indicates that joint selection for beef and dairy traits is possible in the studied population without losses in reproductive traits. Genomic predictions were then performed using single- step genomic best linear unbiased prediction (ssGBLUP) using single-trait models. The performance of genomic prediction (in terms of predictive ability, bias, accuracy of breeding values, rank correlations, and genetic trends) using the ssGBLUP approach compared to the traditional BLUP approach was investigated. This study provided interesting insights into the future application of ssGBLUP in genetic evaluation of Guzerá cattle, especially for dairy traits. The results suggest that ssGBLUP is feasible and can be used in national genetic evaluations for reproductive, dairy, and beef traits in Guzera animals to increase the accuracy of breeding values. However, the number of genotyped animals was not yet sufficient to affect the genetic evaluation in terms of predictive ability and bias. In addition, a third study was conducted to determine the runs of homozygosity (ROH) and calculate the inbreeding coefficients of the animals from the ROH (F ROH ). The inbreeding coefficients from pedigree information (F PED ) were also estimated and the effects of F ROH and F PED on reproductive, dairy and beef traits in Guzerá animals were evaluated. Although the Brazilian population of Guzerá animals has experienced historical events such as the bottleneck effect, inbreeding coefficients were low compared to other cattle breeds, even in younger animals. There was no inbreeding depression in the evaluated traits. The results described in this thesis will contribute to the definition of selection criteria for dual-purpose cattle. In addition, this thesis provides the first results on the impact of incorporating information from SNP markers into genetic evaluations of dairy, reproductive and growth traits in Guzerá cattle (in terms of predictive ability, bias, accuracy of breeding values, rank correlations and genetic trends). In summary, our results show that joint selection for beef and dairy traits is feasible in the population studied, that the inclusion of SNP marker information increases the accuracy of animal breeding values, and that the population maintains low levels of inbreeding even during a bottleneck event without significant effects on the most important traits subject to selection. Keywords: Beef cattle. BLUP. Bos indicus. Dairy cattle. Genetic evaluation. Inbreeding. ssGBLUP. Zebu.