The after-effect relation between stress and strain in a linear viscoelastic material is examined using general principles only. First of all, it is a linear passive system and all results on linear passive systems can be applied. Secondly, thermodynamic principles are invoked. They are the existence of stress equilibrium for constant strain, of welldefined flow properties or equilibrium of strain for constant stress, the existence of asymptotically harmonic stress or strain if the strain or stress, respectively, is a harmonic function after some transients, and finally the existence of positive entropy production in a real process. Only if one looks more closely into the internal processes, wich are going on under an applied stress or strain history, is it possible to give a more detailed characterisation of the after-effect functions: If only even internal variables are excited, one arrives at the usually adopted description of after-effect functions in terms of retardation and relaxation spectra. It may be that odd internal variables, which are connected with some internal inertia, come into play for relatively fast processes only, which would justify their neglect for slow processes. — A very simple mathematical characterisation of viscoelastic materials with pure relaxation behavior is given. The results are derived for isotropic materials; but they can easily be generalized to anisotropic materials.