The Brazilian Unified Health System was created in the late 1980s to ensure free universal access to health care and was funded by taxes and social contributions. The persistent inequity in access to health services in favour of richer individuals in Brazil has been observed in the literature. However, to the best of our knowledge, no measurement of inequality in medicine use or private health insurance (PHI) among children has been performed with longitudinal data. This paper uses inequality indices and their decompositions to analyse the income-related inequalities/inequities in children's health care in the city of Pelotas, Brazil, using longitudinal data following children from 12 to 72 months of age. Our sample with data in all waves has between 1877 and 2638 children (varying according to outcome). We seek to answer three questions: i) How does the inequality/inequity in health care evolve as children grow up? ii) What are the main factors associated with inequality in children's health care? iii) How much of the change in inequality/inequity is explained by mobility in children's health care and income mobility? We found that inequities in health care have their beginnings in early childhood but that there was a reduction in inequity at 72 months of age. Ownership of children's PHI was associated with greater pro-rich inequity in health care. The reduction in inequality/inequity was linked to mobility in the sense that initially poorer children had greater gains in health care (a greater increase in PHI ownership and a lower reduction in medicine use). Despite this improvement among the poorest, apparently, the Brazilian public health service seems to fail to ensure equity in health care use among children, with possible long-term consequences on inequalities in health. •The inequities in health care have their beginnings even in early childhood.•Income and mother's education have a strong contribution in the inequalities.•Private health insurance has strong contribution in inequalities of medicine use.•There was reduction in inequity for children's health care in Pelotas/Brazil.•This improvement for poorest children occurred when they reached 72 months.