The chronology of these Popes cannot be determined with any degree of exactitude by the help of the extant sources. (Catholic Encyclopedia: Pope St. Hyginus) According to Eusebius (Church History, IV, xv.) Hyginus succeeded Telesphorus during the first year of the reign of Emperor Antoninus Pius, i.e. in 138 or 139. Eusebius (Church History, IV, xvi) states that Hyginus's pontificate lasted four years.
