Depression and anxiety are both prevalent among university students. They frequently co-occur and share risk factors. Yet few studies have focused on identifying students at highest risk of first-onset and persistence of either of these conditions. Multicenter cohort study among Spanish first-year university students. At baseline, students were assessed for lifetime and 12-month Major Depressive Episode and/or Generalized Anxiety Disorder (MDE-GAD), other mental disorders, childhood-adolescent adversities, stressful life events, social support, socio-demographics, and psychological factors using web-based surveys; 12-month MDE-GAD was again assessed at 12-month follow-up. A total of 1253 students participated in both surveys (59.2% of baseline respondents; mean age = 18.7 (SD = 1.3); 56.0% female). First-onset of MDE-GAD at follow-up was 13.3%. Also 46.7% of those with baseline MDE-GAD showed persistence at follow-up. Childhood/Adolescence emotional abuse or neglect (OR= 4.33), prior bipolar spectrum disorder (OR= 4.34), prior suicidal ideation (OR=4.85) and prior lifetime symptoms of MDE (ORs=2.33-3.63) and GAD (ORs=2.15-3.75) were strongest predictors of first-onset MDE-GAD. Prior suicidal ideation (OR=3.17) and prior lifetime GAD symptoms (ORs=2.38-4.02) were strongest predictors of MDE-GAD persistence. Multivariable predictions from baseline showed AUCs of 0.76 for first-onset and 0.81 for persistence. 74.9% of first-onset MDE-GAD cases occurred among 30% students with highest predicted risk at baseline. Self-report data were used; external validation of the multivariable prediction models is needed. MDE-GAD among university students is frequent, suggesting the need to implement web-based screening at university entrance that identify those students with highest risk. •13.3% students had first-onset of MDE and/or GAD at 12-month follow-up.•Among students with baseline MDE and/or GAD, 46.7% persisted at 12-month follow-up.•Strongest predictors were lifetime symptoms of MDE-GAD and prior suicidal ideation.•Multivariable models provided AUCs 0.76–0.81 to predict first-onset and persistence.•74.9% onset MDE-GAD cases occur in 30% students at highest predicted baseline risk.