A non-gray theory of extrasolar giant planets (EGPs) and brown dwarfs is presented, covering effective temperatures below 1300 K. This study provides the first comprehensive spectral analysis of these objects down to 100 K, revealing their unique atmospheric and spectral characteristics. The dominant carbon molecule below 1300 K is methane, and nitrogen is primarily ammonia below 600 K. Key spectral features include the Z, J, H, K, M, and N bands, with significant enhancements in flux over blackbody values, particularly in the near-infrared. The infrared colors of these objects are much bluer than previously thought. Clouds of water and ammonia form at temperatures below 400 K and 200 K, respectively. The study also shows that most metals are sequestered below the photosphere, and that a radiative zone is a common feature in substellar objects. The non-gray theory is applied to a wide range of masses, from 0.3 to 70 MJ, and is useful for detecting EGPs and brown dwarfs. The results highlight the importance of non-gray atmospheric models in understanding the evolution and spectral characteristics of these objects. The study also addresses the effects of stellar insolation and the role of clouds in spectral formation. The results are presented in the context of the broader M dwarf/brown dwarf/EGP continuum, with detailed evolutionary models and spectral analysis. The findings have implications for the detection and characterization of substellar objects using ground- and space-based telescopes.A non-gray theory of extrasolar giant planets (EGPs) and brown dwarfs is presented, covering effective temperatures below 1300 K. This study provides the first comprehensive spectral analysis of these objects down to 100 K, revealing their unique atmospheric and spectral characteristics. The dominant carbon molecule below 1300 K is methane, and nitrogen is primarily ammonia below 600 K. Key spectral features include the Z, J, H, K, M, and N bands, with significant enhancements in flux over blackbody values, particularly in the near-infrared. The infrared colors of these objects are much bluer than previously thought. Clouds of water and ammonia form at temperatures below 400 K and 200 K, respectively. The study also shows that most metals are sequestered below the photosphere, and that a radiative zone is a common feature in substellar objects. The non-gray theory is applied to a wide range of masses, from 0.3 to 70 MJ, and is useful for detecting EGPs and brown dwarfs. The results highlight the importance of non-gray atmospheric models in understanding the evolution and spectral characteristics of these objects. The study also addresses the effects of stellar insolation and the role of clouds in spectral formation. The results are presented in the context of the broader M dwarf/brown dwarf/EGP continuum, with detailed evolutionary models and spectral analysis. The findings have implications for the detection and characterization of substellar objects using ground- and space-based telescopes.