We describe the Berkeley extreme-UV airglow rocket spectrometer, which is a payload designed to test several thermospheric remote-sensing concepts by measuring the terrestrial O I far-UV and extreme-UV dayglow and the solar extreme-UV spectrum simultaneously. The instrument consisted of two near-normal Rowland mount spectrometers and a Lyman-alpha photometer. The dayglow spectrometer covered two spectral regions from 980 to 1040 A and from 1300 to 1360 A with 1.5-A resolution. The solar spectrometer had a bandpass of 250-1150 A with an ~ 10-A resolution. All three spectra were accumulated by using a icrochannel-plate-intensified, two-dimensional imaging detector with three separate wedge-and strip anode readouts. The hydrogen Lyman-alpha photometer was included to monitor the solar Lyman-alpha irradiance and geocoronal Lyman-alpha emissions. The instrument was designed, fabricated, and calibrated at the University of California, Berkeley and was successfully launched on 30 September 1988 aboard the first test flight of a four-stage sounding rocket, Black Brant XII.