He was the brother of Gaius Asinius Rufus, son of Gaius Asinius Nicomachus and wife and cousin Julia Quadratilla (or perhaps Asinia Marcellina, descendant of the family of Gaius Asinius Pollio) and paternal grandson of Gaius Asinius Rufus and wife Julia.
Nicomachus was quite young when Aristotle wrote his will, as can be seen from the fact that Nicanor, Aristotle's nephew by his sister Arimneste, is appointed guardian until Nicomachus came of age.
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.