And Nadab and Abihu died before the Lord,...., By flaming fire, as the Targum of Jonathan adds, see Le 10:2; and so were not alive at this time when the account of the priests and Levites was taken:when they offered strange fire before the Lord in the wilderness of Sinai; after the tabernacle was set up, and the service of it begun, and quickly after their unction and consecration: of this strange fire,See Gill on "Nu 10:1";and they had no children; which is observed, partly to show the punishment of them, and the reproach upon their names, that they died childless, and had none to succeed them in the priesthood; for as the Jewish writers observe if they had left any behind them, those would have come into the office before Eleazar and Ithamar; and partly to show that all the priests in succeeding ages sprung from those next mentioned:and Eleazar and Ithamar ministered in the priest's office, in the sight of Aaron their father; in his presence, under his inspection, and by his direction, he seeing and observing that they did everything according to the laws delivered by Moses, relating to, the office of the priesthood; or while he was yet alive, as Aben Ezra, they were concerned with him, and acted under him in the priestly office; and so the Septuagint version renders it, "with Aaron their father" ; but a Jewish writer interprets it in a different manner, "in the room of Aaron their father"; as if it respected not any conjunction with him in the then present exercise of their office in his lifetime, but their succession in it after his death; but the former seems most correct.
Torat Cohanim apud Ceseph Misnah in Maimon. Melachim, c. 1. sect. 7. Chaskuniin in loc. Which is approved by Noldius, p. 731.