Several fractional rheological models containing one or two fractional elements in addition to the classical springs and dashpots have been proposed to describe the dynamic behavior of magnetoactive elastomers (MAEs) in magnetic fields. To test the models, MAEs containing 70, 75 and 80 wt% of carbonyl iron particles with the diameter of 3-5 mu m have been synthesized. Theoretical model parameters have been obtained via fitting experimental frequency dependences of MAE's dynamic modulus measured under dynamic torsion oscillations in linear viscoelastic regime. It has been shown that the simplest rheological models with one fractional element can adequately describe MAEs behavior at low and for some cases high magnetic fields where the main contribution to the MAEs elasticity arises either from polymer network or magnetic particle aggregates, respectively. However, these models fail in describing MAE's dynamics in intermediate magnetic fields where the major restructuring of the magnetic filler particles is expected. The best fitting is realized with two-fractional-element models for a wide range of magnetic fields. The role of two fractional elements in generalized Maxwell model has been interpreted in terms of two main MAE components (namely, polymer network and magnetic particles) whose contributions to material elasticity and viscosity depend considerably on the material composition and magnetic field strength. (C) 2018 Elsevier Ltd. All rights reserved.