A simplified and numerically efficient method to compute radiative flux densities and heating rates in a general circulation model (GCM) is presented. The parameterization extends continuously from the surface up to the lower thermosphere and avoids any merging of radiative heating rates from different schemes, which is usual in comprehensive middle atmosphere GCMs. To investigate coupling processes affecting the whole atmosphere, however, continuous radiative transfer calculations are desirable. In the long-wave regime, frequency-averaged Eddington-type transfer equations are derived for four broad absorber bands. The frequency variation inside each band is parameterized with the Elsasser band model extended by a slowly varying envelope function. This yields additional transfer equations for the perturbation amplitudes which are solved simultaneously together with the mean transfer equations. Deviations from local thermodynamic equilibrium are accommodated in terms of isotropic scattering computed from the two-level model for each band. Solar radiative flux densities are computed for four energetically defined bands using the simple Beer-Bougert-Lambert relation for absorption within the atmosphere. These methods circumvent all the conventionally applied approximations to compute the complicated flux transmission functions that result from formal integration of the radiative transfer equation. The new scheme is implemented in the KĂĽhlungsborn Mechanistic general Circulation Model (KMCM). First test simulations with low resolution (T32L70) and prescribed concentrations of the radiatively active constituents show quite reasonable results and compare satisfactory to other middle atmospheric GCMs. In particular, since we take the full surface heat budget into account by means of a swamp ocean, and since the internal dynamics and turbulent diffusion of the model are formulated in accordance with the conservation laws, an equilibrated climatological radiation budget is obtained at the top of the atmosphere as well as at the surface. Nevertheless we observe a pronounced annual cycle in the radiation budget at the model top with a positive radiative forcing during late NH winter and a balancing negative forcing during late SH winter. This behavior likely reflects the north-south asymmetry in the dynamic poleward heat transport. In the future, the new model configuration will be used with high spatial resolutions to explicitly simulate the interaction of gravity waves with the radiation field.