       In Vivo      6    , J. Azevedo Jr. 3 , J.C. de Sousa 2 , V.D. Timpani 4 , M.A.D. Dias 3 , M.C.A.M. Bink 5  Animal breeding programs for the improvement of   carcass traits are imperative to increase meat quality and productivity. An effort to know the genetic architecture of these traits should be done before their inclusion in a breeding program. Generally, some quantitative traits, such ad, loin-eye area, rump fat thickness and back fat thickness are considered to be influenced by many genes with small effects. However, it was suggested that few genes could be responsible for a great part of the variation of quantitative traits (Lande, R. (1981)). These genes are known as major genes (MG). Carcass traits, generally, are modeled assuming an infinitesimal polygenic model (IPM), having a discreet distribution using a finite polygenic model (FPM) (Thompson, E.A. and Skolmick, M.H. (1977), Fernando, R.L., Stricker, C., Elston, R.L (1994), Lange, K. (1995)), or modeled with a combination of IPM and FPM (Bink, M.C.A.M., Uimari, P., Sillanpää, M.J.  . (2002), Gonçalves, T.M., Oliveira, H.N., Bovenhuis, H.   (2005)), which considers polygenic and oligogenic effects. The aim of this work was to adjust a combined model to describe the genetic architecture of three carcass traits evaluated by real-time ultrasonography in Guzerá cattle.    Ultrasound data from 655 animals were used. Loin-eye area (LEA), rump fat thickness (RFT) and back fat thickness (BFT) images were obtained by positioning the transducer transversely between the 12ª and 13ª ribs, parallelly between 12ª and 13ª rib and at the junction between the   and   muscles, respectively. All ultrasound measurements were performed by a single experienced technician using an Aloka 500V unit with a 3.5 MHz/17.2cm linear transducer (Aloka Co. Ltd – Wallingford, EUA). The combined model (IPM+FPM) adjusted for each trait analyzed was: ~ , ~ ~ ~             + + + = ∑ α β Where: y = is the vector of observations; X = incidence matrix of non-genetic factors, which connects the phenotypes of non-genetic effects; β = is a vector containing the mean (µ) and all non-genetic factors (NID) affecting the characteristics of interest: animal age and body weight at the time of measurement, contemporary group (sex, birth year, birth farm, feed management and date of measurement) and permanent environmental effect; W = incidence matrix of the genetic random direct effects, related to the observations to infinitesimal polygenic effects; u = is the vector of random effects of direct genetic values of animal, the effects of several genes with infinitesimal effect that are not explained by the major gene are computed here; Z MG = incidence matrix that connects the phenotypic information to MG. It is typically unknown, since the genotypes of individuals are not known. However, this matrix can be inferred from the pedigree and phenotype (segregation indicators). It is assumed that the MG is biallelic allowing three different genotypes (AA, Aa and aa) and having genotypic values equal to + α, δ and -α, respectively. The variables α and δ represent the additive and dominance effects of a single gene. The matrix Z size depends on the number of MG in the model; N MG = is the number of major genes. This number is considered a random variable and makes inferences about the distribution from the data analyzed; α MG = is a bidimensional vector for the k th major gene (MG), i.e., additive (a) and dominance (d) effects were adjusted here. It was assumed that the loci for MG are biallelic; e = vector of the normally distributed residual associated to each observation. In this model the presence of a maximum of fifteen and at least one locus for major genes (MG), and one locus of infinitesimal polygenic effect were assumed to explain the genetic variation found. ________________________________________ 1 Animal Science Department’s professor, Federal University of Lavras – Brazil. 2 Animal Science Department’s professor, Federal University of Lavras – Brazil. 3 Animal Science Department’s MSc student, Federal University of Lavras. 4 Animal Science Department’s DSc student, Federal University of Lavras. 5 Biometris, PO Box 100, 6700AC Wageningen, The Netherlands. 6 Support of FAPEMIG.