Final answer:
The Epistle of James and the Epistle of Jude are the two New Testament books that may have been written by a brother of Jesus, according to traditional Christian teachings.
Step-by-step explanation:
The two New Testament (NT) books that may have been written by a brother of Jesus are the Epistle of James and the Epistle of Jude. These texts are among the General Epistles in the Christian New Testament that hold significance for both historical and theological reasons. Though there is some debate among scholars regarding authorship, traditional Christian teaching suggests that James, also known as James the Just, who was a prominent figure in the early Church, authored the book bearing his name. Similarly, Jude, another brother of Jesus, is traditionally considered the author of the brief epistle that bears his name.