This thesis attempted to provide estimates of (co)variance components, heritabilities and genetic and phenotypic correlations between traits of economic importance in two breeds of hill sheep, the Welsh Mountain and the Beulah
Speckled Face. Maternal effects were important in univariate models for weight and ultrasonically-scanned traits, and generally a model that included direct additive effect, additive maternal genetic effect, maternal permanent
environmental effect and maternal temporary environmental effect was found to be the most appropriate. Direct heritabilities (h2) for eight-week weight (EWW), scan weight (SW), ultrasonically-scanned muscle (MD), ultrasonically-scanned fat depth (FD), litter size born (LSB), litter size reared (LSR) and total litter weight at eight-weeks (LW) were 0.18, 0.25, 0.24, 0.21, 0.13, 0.09, and 0.11 respectively in the Welsh Mountain, and 0.09, 0.18, 0.19, 0.20, 0.13, 0.08, and
0.10 respectively in the Beulah Speckled Face. Direct heritability for mature weight (MW) was 0.52 in the Welsh Mountain. All genetic correlations between weight and ultrasonically-scanned traits were positive. Genetic correlations
among weight traits were high in both breeds. Genetic correlations between litter traits and other (weight and ultrasonic) traits were positive in all but one case. LSB was strongly correlated with LSR but both were negatively or weakly
correlated with LW. Cytoplasmic factors as a source of inheritance in weight and ultrasonically-scanned traits was investigated in the Welsh Mountain breed.
No effect of cytoplasmic inheritance was apparent for EWW and MD, and the effect was generally non-significant for SW and FD. Scrapie genotype data from one Welsh Mountain flock were examined. Ten genotypes, four alleles (ARH,
ARQ, ARR, and VRQ) covering all five NSP risk categories were present. There was little evidence of association between PrP genotypes and EWW, SW, MD and FD, and the selection of ARR homozygous did not appear detrimental to breeding progress in these traits.