Claudius was the son of an earlier Tiberius Claudius Cleobulus (c. 135 – c. 180) and his wife Acilia, the daughter of Manius Acilius Glabrio Gnaeus Cornelius Severus and his wife Faustina. He married his first cousin, Acilia Frestana, who was the daughter of Manius Acilius Glabrio, consul in 186, and paternal niece of Acilia. Tiberius Claudius Cleobulus and his wife Acilia Frestana together had Claudia Acilia Priscilliana, who would later marry Lucius Valerius Messalla.[2][3] He also had a son, Claudius Acilius Cleobulus.
Dondin-Payre, Monique (1993). Exercice du pouvoir et continuité gentilice : les Acilii Glabriones : du IIIe siècle av. J.-C. au Ve siècle ap. J.-C (in French). Rome: École française de Rome. ISBN9782728302710.
Lehmann, Clayton Miles; Holum, Kenneth G. (1999). The Greek and Latin Inscriptions of Caesarea Maritima. Atlanta, Ga.: Scholars Press. ISBN9780897570282.
Mennen, Inge (2011). Power and Status in the Roman Empire, AD 193-284. Leiden: Brill. ISBN9789004203594.
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