Research has shown associations between parental and child mental health problems. However, there is a paucity of Swedish studies on this topic. Investigating this link in a Swedish context could inform preventive interventions aimed at reducing mental health problems in affected families. This longitudinal cohort study aimed to explore the association between parental mental health problems and children's subsequent mental disorders in Sweden. We used data on children, 3-5 years old, whose mothers (n = 6379) and fathers (n = 6218) had responded to the 12-item General Health Questionnaire for assessment of parental mental health problems using a cut-off of >= 12 points. The children were followed for approximately seven years with regard to subsequent mental disorders, collected from the Swedish National Patient Register. The associations between parental mental health problems and children's mental disorders were explored through Cox-regression models. In unadjusted Cox regression models, mothers (HR: 1.63, 95% CI: 1.37-1.94) and fathers (HR: 1.36, 95% CI: 1.12-1.65) with mental health problems were more likely to have children diagnosed with a subsequent mental disorder than mothers and fathers with no mental health problems. In adjusted models controlling for children's emotional and behavioral problems and parental sociodemographic factors, the associations remained significant for mothers' mental health problems (AHR: 1.33, 95% CI: 1.12-1.59), but not for fathers' (AHR: 1.14, 95% CI: 0.93-1.40). Children with emotional and behavioral problems, whose parents were single or living apart and whose parents had lower educational levels also had an elevated risk of being diagnosed with a mental disorder. Maternal mental health problems and child emotional and behavioral problems during the preschool years may serve as risk factors for subsequent child mental disorders. Assessment of these problems at child health services in Sweden could facilitate delivery of interventions to promote parental and child mental health.