  This paper deals with the mathematical modelling of large strain
magneto-viscoelastic deformations. Energy dissipation is assumed to occur both
due to the mechanical viscoelastic effects as well as the resistance offered by
the material to magnetisation. Existence of internal damping mechanisms in the
body is considered by decomposing the deformation gradient and the magnetic
induction into `elastic' and `viscous' parts. Constitutive laws for material
behaviour and evolution equations for the non-equilibrium fields are derived
that agree with the laws of thermodynamics. To illustrate the theory the
problems of stress relaxation, magnetic field relaxation, time dependent
magnetic induction and strain are formulated and solved for a specific form of
the constitutive law. The results, that show the effect of several modelling
parameters on the deformation and magnetisation process, are illustrated
graphically.
