Models were developed which allowed for sex difference in the expression of autosomal polygenes, differences in the impact of the paternal and maternal environment on male and female offspring, and for the complex consequences of assortative mating on the correlations among loci and between genes and environment. Computer simulations were used to decide which kinds of gender-dependent effects could be resolved with particular constellations of relatives, and to address problems of power and bias resulting from errors of model-specification. The methods developed were applied to data from extensive data already gathered from twins and their relatives to determine the importance of sex differences in genetic and environmental causes of variation in measured aspects of cardiovascular risk including weight, body-mass index, family history of CV disease, smoking, alcohol consumption, exercise, diet, psychosocial variables and lifestyle.