Simplified band models are developed for methane (CH4) and nitrous oxide (N2O) bands in the longwave radiation spectrum. The band models are then employed in a radiation model to calculate the seasonally and latitudinally varying contributions of CH4, and N2O to the radiative energy balance of the earth-troposphere system. From the energy balance calculations, it is concluded that the longwave opacity (i.e., the so-called “greenhouse effect”) due to present-day observed concentrations of CH4. and N2O contribute nearly 2 K to hemispherical mean surface temperature with possible larger contributions to polar surface temperatures. The paper also discusses stratospheric effects of CH4 and N2O and examines the sensitivity of tropospheric radiation energy balance to large increases in CH4 and N2O. Abstract Simplified band models are developed for methane (CH4) and nitrous oxide (N2O) bands in the longwave radiation spectrum. The band models are then employed in a radiation model to calculate the seasonally and latitudinally varying contributions of CH4, and N2O to the radiative energy balance of the earth-troposphere system. From the energy balance calculations, it is concluded that the longwave opacity (i.e., the so-called “greenhouse effect”) due to present-day observed concentrations of CH4. and N2O contribute nearly 2 K to hemispherical mean surface temperature with possible larger contributions to polar surface temperatures. The paper also discusses stratospheric effects of CH4 and N2O and examines the sensitivity of tropospheric radiation energy balance to large increases in CH4 and N2O.