We describe the system of Tomographic Extreme Ultraviolet (EUV) SpectrographS (TESS) that are the primary instruments for the Tomographic Experiment using Radiative Recombinative Ionospheric EUV and Radio Sources (TERRIERS) satellite. The spectrographs were designed to make high-sensitivity {80 counts/s)/Rayleigh [one Rayleigh is equivalent to 10(6) photons/(4pi str cm(2)s)}, line-of-sight measurements of the oi 135.6- and 91.1-nm emissions suitable for tomographic inversion. The system consists of five spectrographs, four identical nightglow instruments (for redundancy and added sensitivity), and one instrument with a smaller aperture to reduce sensitivity and increase spectral resolution for daytime operation. Each instrument has a bandpass of 80-140 nm with approximately 2- and 1-nm resolution for the night and day instruments, respectively. They utilize microchannel-plate-based two-dimensional imaging detectors with wedge-and-strip anode readouts. The instruments were designed, fabricated, and calibrated at Boston University, and the TERRIERS satellite was launched on 18 May 1999 from Vandenberg Air Force Base, California.