Excessive oxidative stress-generated nucleoside damage seems to play a key role in bipolar disorder (BD) and may present a trait phenomenon associated with familial risk and is one of the putative mechanisms explaining accelerated atherosclerosis and premature cardiovascular diseases (CVD) in younger patients with BD. However, oxidative stress-generated nucleoside damage has not been studied in young BD patients and their unaffected relatives (UR). Therefore, we compared oxidative stress-generated damage to DNA and RNA in young patients newly diagnosed with BD, UR, and healthy control individuals (HC). Systemic oxidative stress-generated DNA and RNA damage levels were compared by analyzing urinary levels of 8-oxo-7,8-dihydro-2′-deoxyguanosine and 8-oxo-7,8-dihydroguanosine in participants aged 15–25 years, including 133 patients newly diagnosed with BD, 57 UR, and 83 HC. Compared with HC, damage to DNA was 21.8% higher in BD patients (B = 1.218, 95% CI = 1.111–1.335, p = <0.001) and 22.5% higher in UR (B = 1.225, 95% CI = 1.090–1.377, p = <0.002), while damage to RNA was 14.8% higher in BD patients (B = 1.148, 95% CI = 1.082–1.219, p = <0.001) and 14.0% higher in UR (B = 1.140, 95% CI = 1.055–1.230, p = < 0.001) in models adjusted for sex and age after correction for multiple comparison. Levels did not differ between patients with BD and UR. Our findings support higher oxidative stress-generated nucleoside damage being a trait phenomenon in BD associated with familial risk and highlight the importance of early diagnosis and treatment to prevent illness progression and development of premature CVD.