Police say it started as an argument on Durham school bus that was transporting students from Hillside High School.
Bus number 94 was near the intersection of Fayetteville and Pilot streets around 2:52 p.m. when the incident happened.
According to a preliminary investigation, a 14-year-old stabbed a 15-year-old in the back with a pocket knife.
The teen was taken to Duke Medical Center in serious condition. His injuries do not appear to be life threatening.
The 14-year-old is in police custody.
