In this article, the results of a study of the magnetic dynamics of superparamagnetic iron oxide nanoparticles (SPIONs) with chitosan and polyethylene glycol (PEG) coatings are reported. The materials were prepared by the co-precipitation method and characterized by X-ray diffraction, dynamic light scattering and scanning transmission electron microscopy. It was shown that the cores contain maghemite, and their hydrodynamic diameters vary from 49 nm for PEG-coated to 200 nm for chitosan-coated particles. The magnetic dynamics of the nanoparticles in terms of the function of temperature was studied with magnetic susceptometry and Mössbauer spectroscopy. Their superparamagnetic fluctuations frequencies, determined from the fits of Mössbauer spectra, range from tens to hundreds of megahertz at room temperature and mostly decrease in the applied magnetic field. For water suspensions of nanoparticles, maxima are observed in the absorption part of magnetic susceptibility and they shift to higher temperatures with increasing excitation frequency. A step-like decrease of the susceptibility occurs at freezing, and from that, the Brown's and Néel's contributions are extracted and compared for nanoparticles differing in core sizes and types of coating. The results are analyzed and discussed with respect to the tailoring of the dynamic properties of these nanoparticle materials for requirements related to the characteristic frequency ranges of MRI and electromagnetic field hyperthermia.