The objective of this study was to analyse the relations between the function of openness to the world, family functioning and child behaviour. In order to do that, a quantitative research was conducted with 171 biparental families from the South Region of Brazil, with children from four to six years of age. Two association hypotheses were formulated: The function of openness to the world and family functioning positively influence child's strengths and negatively influence their difficulties; Family functioning and the function of openness to the world are positively related, and this relation has an influence on child behaviour, so as to increase strengths and reduce difficulties. Results indicate associations between the phenomena and that it is necessary to consider the interaction between the function of openness to the world and family functioning to better understand child behaviour.