Childhood anxiety and depressive symptoms may be influenced by symptoms of attention deficit/hyperactivity disorder (ADHD). We investigated whether parent- and teacher-reported anxiety, depressive and ADHD symptoms at age 3 years predicted anxiety disorders and/or depression in children with and without ADHD at age 8 years. This study is part of the longitudinal, population-based Norwegian Mother, Father and Child Cohort Study. Parents of 3-year-olds were interviewed, and preschool teachers rated symptoms of anxiety disorders, depression and ADHD. At age 8 years (n = 783), Child Symptom Inventory-4 was used to identify children who fulfilled the diagnostic criteria for anxiety disorders and/or depression (hereinafter: Anx/Dep), and ADHD. Univariable and multivariable logistic regression analyses were used. In the univariable analyses, parent-reported anxiety, depressive and ADHD symptoms, and teacher-reported anxiety symptoms at age 3 years all significantly predicted subsequent Anx/Dep. In the multivariable analyses, including co-occurring symptoms at age 3 years and ADHD at 8 years, parent-reported anxiety and depressive symptoms remained significant predictors of subsequent Anx/Dep. At age 3 years, regardless of ADHD symptoms being present, asking parents about anxiety and depressive symptoms, and teachers about anxiety symptoms, may be important to identify children at risk for school-age anxiety disorders and/or depression.