Clustered (multi-core) magnetic fluids provoke a considerable interest of researchers and practitioners, because they are very promising for various technical and biomedical applications. These fluids contain clusters (clustered particles), which, in turn, consist of ferromagnetic nanoparticles retained together by a polymer shell. The typical size of a cluster varies from a few tens to several hundreds of nanometers, while the sizes of individual single-domain ferroparticles of which it is composed vary from 5 to 12 nm. The rheological phenomena in such fluids (strong magnetorheological effect and slow viscoelastic relaxation) are predetermined by the association of the clustered particles under the action of an external magnetic field into heterogeneous structures and aggregates and the dynamics and disruption of these aggregates in macroscopic deformational flows. In this work, we propose a theoretical model for viscoelastic effects in clustered magnetic fluids. The model is based on the idea of aggregating composite particles into linear chain-like aggregates. In the order of magnitude, the theoretical results agree with experimental data.