Luke 2:2

In speaking of the census that took Joseph and Mary to Bethelehm, Luke says, “This registration first took place while Quirinius was governing Syria” (αὕτη ἀπογραφὴ πρώτηa ἐγένετο ἡγεμονεύοντος τῆς Συρίας Κυρηνίου).

The difficult phrase is the genitive absolute, “Quirinius governing Syria” (ἡγεμονεύοντος τῆς Συρίας Κυρηνίου). ἡγεμονεύω occurs only here in the NT and apparently takes a direct object in the genitive.