Objective: To determine the Brazilian Universal Health Care System (Sistema Único de Saúde [SUS]) health services integration and accessibility of care for children with brain paralysis. Methods: This was an exploratory, descriptive, qualitative study. Six families with children who have brain paralysis caused by asphyxia neonatorum and who were residents in Rio Grande, RS, participated in the study. Data were collected in the participants' home through a semi-structured interview. Results: Families had difficulties with the SUS health services' integration and accessibility. There were gaps between the care the SUS proposes to provide and the care the families actually received. Conclusion: The lack of access to adequate care extends beyond primary care and not always observes reference and contra reference.