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He was the nephew (according to Zonaras xii.24) or the cousin (according to Historia Augusta, which lists him among the Thirty Tyrants) of Odaenathus, who had taken control of the Eastern provinces after the defeat and capture of Emperor Valerian by Shapur I of the Sassanid Empire.
As the title suggests, it might have been a continuation of the Annals by Tacitus: in fact, in the often unreliable Historia Augusta, inside the book devoted to the life of the Roman emperor Aurelian (270–275), it is included a letter from Aurelian to queen Zenobia that the author claims reported by a Nicomachus; it is therefore possible that Nicomachus' work was a continuation of Tacitus' until, at least, Aurelian.
The (dubious) Historia Augusta equally has a short description of Victorinus Junior, allegedly the son of Victorinus, who was appointed emperor by his family the day his father was murdered, and would have been killed immediately afterwards by the troops.