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Magnetoactive elastomers (MAEs) consisting of soft polymer matrices filled with magnetic nano- or microparticles belong to a class of so-called smart materials being able to change their physical properties in response to various external stimuli. In case of MAEs such stimulus is a magnetic field. When a magnetic field is applied to MAEs magnetic filler particles start to interact and if the matrix is soft enough these interactions can cause particle restructuring leading to a change in a number of physical properties of MAEs. In particular, MAEs demonstrate a huge increase of their elastic modulus [1]. To obtain a highly responsive MAE, one has to decrease the elastic modulus of the polymer matrix or to increase the saturation magnetization of magnetic filler because larger matrix deformations will be required to equilibrate the elastic and magnetic forces acting between magnetic particles. To make softer elastomers with a modulus lower than 10kPa solvents are usually employed. In case of silicone elastomers the solvent or plasticizer is silicone oil, in case of hydrogels it is usually water. In this work we developed a new type of silicone-based elastomers whose modulus can be considerably decreased by using specially designed cross-links containing dangling chains.The presence of dangling chains dilutes the matrix causing a decrease of its elastic modulus without any low-molecular-mass additives. MAEs of various compositions (various concentrations of cross-linking agent and magnetic filler) were synthesized and their rheological properties have been studied depending on the strength of the external magnetic field. It has been shown that the initial modulus of the composite can be varied in the range of 2-50 kPa and the magnetic response of the obtained materials can reach two orders of magnitude in relatively low magnetic fields. The effect of the dangling chains on the viscoelastic behavior of both unfilled matrices and composites is discussed.