Mapping quantitative trait loci in outbred populations is important since development of inbred lines in livestock species is usually not feasible. Traditional genetic mapping methods, such as Least Squares and Maximum Likelihood, cannot fully accommodate complex pedigree structures, and more sophisticated methods such as Bayesian analysis are very demanding computationally. In this thesis, an alternative approach based on a Residual Maximum Likelihood method for estimation of position and variance of one or two linked QTLs and of additive polygenic and residual variances is presented. The method is based on a mixed linear model including polygenic and random QTL allelic effects. The variance-covariance matrix of QTL allelic effects and its inverse is computed conditional on incomplete information from multiple linked markers. The method is implemented using interval mapping and a derivative-free algorithm, where the required coefficient matrix of the Mixed Model Equations is derived from a Reduced Animal Model. simulation studies based on a granddaughter design with 2000 sons, 20 sires and 9 ancestors were performed to evaluate parameter estimation and power of QTL detection. Daughter Yield Deviations of sons were simulated under three QTL models, a biallelic, a multiallelic (10 alleles), and a normal-effects model. A linkage group of five or nine markers located on the same chromosome was assumed, and genotypes were available on sons, sires and ancestors. Likelihood ratio statistics were used to test for the presence of one or two linked QTLs. Parameters were estimated quite accurately for all three QTL models, showing that the method is robust to the number of alleles at the QTL. The effect of considering or ignoring relationships in the analyses did not have a major impact on parameter estimates but reduced the power of QTL detection. In general, power tended to decrease as the number of sons per sire, QTL contribution to additive genetic variance, or distance between QTLs was reduced. The method allowed for detection of a single QTL explaining 25% of the additive genetic variance, and for detection of two QTLs when jointly they accounted for 50% or 12.5% of the additive genetic variance. Although the REML analysis is an approximate method incorporating an expected covariance matrix of the QTL effects conditional on marker information, it is a computationally less expensive alternative to Bayesian analysis for accounting for the distribution of marker-QTL genotypes given marker and phenotypic information. For the designs studied, parameters were estimated accurately and QTLs mapped with satisfactory power.