The data received from the thermal infrared channel 4 (~10.3--11.3 μm) and channel 5 (~11.5--12.5 μm) of the advanced very high resolution radiometer (AVHRR) flown on the National Oceanic and Atmospheric Administration (NOAA) Polar-Orbiting Operational Environmental Satellites provide only a linear estimate of the actual radiance. We describe here a simple procedure, which incorporates data from prelaunch calibration tests, to correct the linear estimates for the nonlinear response of the channels 4 and 5 Mercury-Cadmium-Telluride (Hg-Cd-Te) sensors. The procedure applies a nonzero radiance of space concept to specify the form of the linear radiance estimate. This linear radiance is nearly independent of the operating temperature of the AVHRR and is the sole input to the correction algorithm. Additionally, it is demonstrated with NOAA 14 data that this calibration procedure resolves discrepancies found in the prelaunch data which can affect the calibration accuracy of channel 3 (~3.55--3.95 μm), which possesses a linear response, as well as channels 4 and 5. When applied to independent sets of prelaunch calibration data, this procedure reproduces the laboratory-measured temperature data to within an accuracy of 0.1¿--0.2 ¿K. Comparison with nonlinearity corrections based on different procedures points to the superior applicability of the present results over the entire range of Earth-scene temperatures measured by the AVHRR in orbit. This accuracy is particularly important when these three infrared channels are used in multichannel algorithms to generate environmental parameters such as sea surface temperature. The algorithm coefficients and values of the nonzero radiance of space required to calculate the nonlinearity radiance corrections are given for the AVHRRs on NOAA 7, 9, 10, 11, 12, and 14 spacecraft. ¿ 1998 American Geophysical Union