Simulations were used to study the influence of model adequacy and data structure on the estimation of genetic parameters for traits governed by direct and maternal effects. To test model adequacy, several data sets were simulated according to different underlying genetic assumptions and analysed by comparing the correct and incorrect models. Results showed that omission of one of the random effects leads to an incorrect decomposition of the other components. If maternal genetic effects exist but are neglected, direct heritability is overestimated, and sometimes more than double. The bias depends on the value of the genetic correlation between direct and maternal effects. To study the influence of data structure on the estimation of genetic parameters, several populations were simulated, with different degrees of known paternity and different levels of genetic connectedness between flocks. Results showed that the lack of connectedness affects estimates when flocks have different genetic means because no distinction can be made between genetic and environmental differences between flocks. In this case, direct and maternal heritabilities are under-estimated, whereas maternal environmental effects are overestimated. The insufficiency of pedigree leads to biased estimates of genetic parameters.