The 1H NMR spectra and spin dynamics of the host system in liquid and solid suspensions of γ-Fe2O3 nanoparticles are reported. Significant line broadening of 1H NMR spectra and growing relaxation rates were observed with increased concentration of nanoparticles in liquid systems, with the relation T1/T2 depending on the particular host. Solid systems demonstrate inhomogeneous broadening of the spectra depending on the nanoparticle concentration and practically no dependence of T1 upon the nanoparticle concentration. In variable temperature experiments, significant increase in the relaxation rates was observed in the liquid systems. The experimental results are explained in terms of the self-diffusion as a predominating source of the spin-lattice relaxation. The effective radius of relaxation in the systems in study is estimated.