Broadcasting on 96.1 FM, XEUN-FM is owned by the National Autonomous University of Mexico (UNAM) as a sister to XEUN-AM 860 and XHUNAM-TDT 20.

XEUN-FM signed on July 16, 1959, from a transmitter located on the Torre Rectoría (Rectory Tower), broadcasting with 1 kW of power.

[2] XEUN-FM's power was increased to 50 kW when the station moved to new facilities in 1976.

In 1992, the FM station moved to a new tower in Ajusco, on land that had been donated to UNAM in 1986 by the government of the Federal District; the move decreased the station's power to 35 kW, which then increased to its current 100 kW with another new transmitter in 1995.

On March 25, 2020, as a contingency due to the COVID-19 pandemic, Radio UNAM began simulcasting its FM programming on AM until further notice.