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Introduction Cognitive impairment commonly occurs in hemodialysis patients, with vascular disease potentially implicated in its pathogenesis. However, the relationship of detailed vascular assessment with cognitive function in patients new to hemodialysis has not been demonstrated. Methods In a prospective study of incident hemodialysis participants enrolled in the Predictors of Arrhythmic and Cardiovascular Risk in ESRD (PACE) study, we determined aortic stiffness by pulse-wave velocity (PWV), systemic arterial stiffness by the augmentation index (AIx) and central pulse pressure (cPP), and examined their associations with cognitive processing speed, executive function, and global cognitive impairment measured by the Trail making test A (TMTA), Trail making test B (TMTB), and the modified Mini-Mental State Exam (3MS). Results Mean baseline age was 55 ± 13 years, 58% were male, 72% were African American, 35% had coronary artery disease, 55% had diabetes, and 10% had cognitive impairment. At baseline, higher PWV and cPP were associated with a longer TMTA, and a higher PWV was associated with a longer TMTB, but the associations were attenuated after multivariable adjustment. At 1 year, PWV was not independently associated with TMTA, TMTB, or 3MS. However, unadjusted and adjusted analyses revealed every 10% increase in AIx and 10 mm Hg increase in cPP were associated with longer TMTB (time difference AIx : 0.14; 95% confidence interval [CI]: 0.02−0.25 log-seconds; time difference cPP : 0.11; 95% CI: 0.05−0.17 log-seconds) and global cognitive impairment (odds ratio [OR] AIx : 10.23; 95% CI: 1.77−59.00; OR cPP : 2.88; 95% CI: 1.48−5.59). Discussion Higher AIx and cPP, which are indicative of abnormal wave reflections in distal vessels, are associated with, and might contribute to, declining cognitive function in patients starting hemodialysis.