Reducing and stabilizing abilities of three poly(ethylene glycol) (PEG) samples modified with primary amino groups in one or two terminal positions of the polymer chains, as well as with dendrons based on L-aspartic acid in both terminal positions of the polymer chains, have been studied. Stable dispersions of silver nanoparticles have been formed at room temperature in aqueous solutions of AgNO3 in the presence of the modified PEGs without additional reducing agents. Spectrophotometric examinations have shown that an increase in the number of amino groups per polymer molecule results in accelerating the formation of nanoparticles and improving the stabilizing ability of the modified PEGs. Molecular hydrodynamic methods (analytical centrifugation and dynamic light scattering) have been used to determine the absolute values of the molecular mass of silver nanoparticles stabilized with dendronized PEGs and the hydrodynamic sizes of the particles. Molecular hydrodynamics and electron microscopy have yielded interconsistent estimates of silver nanoparticle sizes.