Chronic heavy alcohol use may lead to permanent brain damage, cognitive impairment, and dementia. While the link between alcohol use and crime is strong, virtually no research exists on the criminal behavior of patients with the alcohol-related neurocognitive disorders of Wernicke-Korsakoff syndrome (WKS) and alcohol-related dementia (ARD). The study population included all persons diagnosed with WKS (n = 1149) or ARD (n = 2432) in Finland in 1998-2015. Data on diagnoses, mortality, and crime were obtained from Finnish nationwide registers. Crime incidences were calculated 4 years before and after diagnosis. Crime types, incidences, and mortality were compared between disorders and with the general population. Altogether 35.6% of WKS patients and 23.6% of ARD patients had committed crimes in the 4 years preceding diagnosis, most commonly property and traffic crimes, followed by violent crimes. The incidence of criminal behavior decreased significantly after diagnosis; in WKS patients, the standardized criminality ratio (SCR), the ratio of observed to expected number of crimes (95% CI), was 3.91 (3.72-4.10) in 4 years before and 2.80 (2.61-3.00) in 4 years after diagnosis. Likewise, in ARD patients, the SCRs were 2.63 (2.51-2.75) before and 0.84 (0.75-0.92) after diagnosis. No significant difference emerged in mortality between persons with and without a criminal history. Persons with alcohol-related neurocognitive disorders frequently engage in criminal behavior prior to diagnosis, especially multiple offending. In the 4 years before and after diagnosis, crime rates declined in a linear fashion, with a marked reduction after diagnosis.