Objective: To analyze the development of acute health problems in moderate and late premature babies in the first month of life. Method: Cross-sectional / epidemiological study with a quantitative approach with 123 moderate and late preterm newborns (NB) in a hospital in southern Brazil. Obstetric, neonatal and socioeconomic variables were collected during hospitalization, while the instrument on acute health problems was applied at the end of the first month of life by telephone contact. For the analysis, tests were used to compare the frequency between the dependent variables and the outcome (Chi-Square and Fisher). A p-value less than or equal to 5% (p≤0.05) was considered a significant statistical association. Results: From the data analysis of 123 newborns, the occurrence of at least one health problem was identified in 96.7% of premature infants. Vomiting was the most frequent health problem. The development of acute health problems, mainly respiratory, at the end of the neonatal period was associated with: birth weight, Apgar 1st min <7 and Apgar 5th min <7, need for neonatal resuscitation, hospitalization in intensive care, type of diet, in addition to associations with the patients' socioeconomic characteristics. Conclusion: Neonatal risk and vulnerability factors are associated with the development of acute respiratory disorders in the first month of life in moderate and late preterm infants, giving rise to greater attention in the monitoring of the studied group.