During runaway discharges in TEXTOR, intense infrared (IR) radiation is-emitted in the electron flow direction. This can only be explained by synchrotron radiation of fast electrons. The observed spectral dependence is consistent with electrons of 25-30 MeV energy; the intensity corresponds to about 1016 electrons or to an electrical current of 40 kA. From the spatial structure of the observed IR pattern, new insight into the spatial distribution of the runaway electrons and their perpendicular momentum can be gained. The runaway electrons populate a torus with a diameter of 0.5-0.6 m, which is slightly larger than the plasma radius; the perpendicular momentum is determined from the vertical extent of the IR pattern and amounts to about 5 m0c. The transformation rate of electrons to runaways can be estimated from the time delay of the IR signal as 2 × 10−4 s−1; this agrees with theoretical expectations derived from the ratio of the electrical field strength to the critical field strength. In TEXTOR, runaways are confined up to energies of 50 MeV, which is just below the limit where a phase should exist in which runaways radiate as much energy as they gain per turn.