The main objectives of this study were to develop and evaluate statistical methods to map quantitative trait loci (QTL) for polygenic binary traits based on genetic markers in half-sib family designs. Generalized Linear Model Interval Mapping method (GLMIM) was developed based on threshold models. Through simulation, the GLMIM was compared with Regression Interval Mapping (RIM) under single and multiple half-sib designs, and with and without the presence of systematic environmental effects (fixed effects). For analyses with and without fixed effects, GLMIM and RIM gave similar estimates of QTL parameters (effect and location) and of power to detect a QTL. For designs with low power, there were small but significant biases in QTL parameter estimates. Accuracy and power of QTL mapping was significantly lower for binary data than for Normal data. Presence of fixed effects reduced power and accuracy of QTL parameters for binary data but not for Normal data. Marker Regression Mapping (MRM) was investigated as an alternative method to interval mapping for Normally distributed traits and extended to half-sib family designs with uncertain transmission of marker alleles. MRM is based on regression of phenotype on paternal marker allele transmission probabilities. With the presence of one QTL in the marker interval, it was shown that expected values of regression coefficients for the flanking markers contained all information about the position and the effect of QTL and were independent of the probability of marker allele transmission. The MRM method for Normal data was extended to binary data by developing a Generalized Linear Model Mapping (GLMM) method based on threshold theory with regression on flanking markers. Through simulation, it was shown that marker regression and interval mapping methods were identical for linear as well as threshold models, and that MRM and GLMM were similar in power and in bias and accuracy of QTL parameters. The main conclusion from this thesis is that QTL mapping for binary traits in half-sib designs based on interval or marker regression mapping gives similar results for linear and threshold models. A wider range of situations and designs must, however, be investigated to authenticate such similarity. Marker regression methods can be used for QTL mapping in practice because they are equivalent to interval mapping methods but computationally simpler.