Genetic parameters for growth, parasite resistance and heat tolerance in zebu-cross cattle in a tropical environment were estimated by restricted maximum likelihood procedures using various forms of an animal model. Heritability estimates for direct additive genetic effects for liveweights at birth, weaning, 12 and 18 months were 0.61, 0.20, 0.25 and 0.26, respectively and corresponding maternal additive genetic effects were 0.11, 0.32, 0.20 and 0.09. Estimates of genetic correlations between direct and maternal additive genetic effects were zero. Weight gains during the dry season were genetically uncorrelated or slightly negatively correlated to birth weight, preweaning weight gain or gains during the wet season. Heritability estimates for rectal temperature, numbers of ticks, buffalo flies and worms were 0.19, 0.34, 0.06 and 0.28, respectively, with corresponding repeatability estimates of 0.23, 0.45, 0.06 and 0.29. Phenotypic correlations between adaptive traits (heat tolerance and parasite resistance) and growth traits were low. Genetic correlations between growth and rectal temperature were negative. Genetic correlations of growth traits with worm and fly burdens were positive and with tick burdens were zero. It was concluded that in reasonably adapted genotypes, selection for growth in the Australian tropics would result in improved heat tolerance and reduced resistance to parasites. The effect of genotype on parameter estimates is discussed.