While Alzheimer disease (AD) is considered a neurodegenerative disorder, the importance of chromosome instability in non-neuronal cells is equally important, not only for shedding light on the etiology of the disease, but also for possible diagnostic purposes and monitoring the progress of the disease. Here, we evaluated the frequency of DNA damage and expression of premature centromere division (PCD) in peripheral blood lymphocytes of sporadic AD patients, age-matched and young controls. The results show that in male patients with AD, the frequencies of PCD and DNA damage were significantly greater (88%, p < 0.01 and 38%, p < 0.05, respectively) than in age-matched control group. AD females had significantly increased frequency of PCD (134%, p < 0.01) as well as a higher frequency of DNA damage (37%, p < 0.05). Ageing per se, both in males and females, shows significant increase of percentages of PCD (2.3 times, p < 0.01 and 2.8 times, p < 0.01, respectively) and DNA damage (63%, p < 0.01 and 50%, p < 0.01, respectively) comparing with young controls. In addition, a strong (R2 = 0.873, n = 6) and significant (p < 0.01) correlation between the frequencies of PCD and DNA damage was found in all examined groups. We may conclude that the increases in both parameters evaluated in this study are not only associated with normal ageing processes, but are markedly and significantly intensified in AD pathogenesis. Thus, our data support the view that AD is a generalized systemic disease, at least as for the increased DNA damage and PCD incidence in peripheral blood cells.