Objective: This study aims to test whether recent increases in the reported prevalence of opioid-use disorder in the United States occurred across all age groups (period effect), consistently only among younger age groups (age effect), or varied according to year of birth (cohort effects). Method: Joint analysis of data from the 1991-1992 National Longitudinal Alcohol Epidemiologic Survey (NLAES) and the 2001-2002 National Epidemiologic Survey on Alcohol and Related Conditions (NESARC), focusing on individuals ages 18-57, grouped by 10-year age intervals. Sample sizes for the present analyses were 30,846 for the NLAES and 31,397 for the NESARC. Prevalence of lifetime and past-year prescription opioid-use disorder resulting from nonmedical use (abuse and dependence) was examined. Results: Within birth cohorts, prevalence of lifetime prescription opioid-use disorder increased during the 10 years between surveys, indicating the importance of age effects. In addition, lifetime and past-year prevalence of prescription opioid-use disorder was higher among more recent birth cohorts as compared with earlier birth cohorts, indicating the importance of cohort effects. Consistent with a period effect, cross-cohort comparisons showed that risk for prescription opioid-use disorder has increased for all individuals regardless of their birth cohort membership from the NLAES to the NESARC survey. Conclusions: Findings suggest that more problems (abuse and dependence) may emerge as prescription opioid users get older and that more recent birth cohorts are at higher risk for prescription opioid problems.