The model of viscoelastic body is considered aiming to describe a wider variety of phenomenological situations. Accordingly, different concurring effects are coupled with viscoelasticity to take into account the combined mechanical response to different effects. Specifically, the classical model of viscoelasticity, is generalised to describe new magnetically sensible materials coupling the viscoelasticity with a magnetisation equation. Key property of the viscoelastic behaviour is the relaxation function G. The classical regularity assumptions are the framework to start with. A further generalisation consists in the introduction in the model of thermal effects. Indeed, a realistic description of the mechanical response of a material in most cases cannot disregard thermal effects further to mechanical and magnetic ones. In this framework, magneto-viscoelastic materials, for instance gels in which micro-particles magnetically sensible are inserted and thermo-magneto-viscoelastic ones, i.e. the same gels when also the thermal effects are taken into account, are considered. In such cases, the mechanical behaviour of the material, respectively, is influenced also by by an external magnetic field or also by the temperature.