Impact of the nanoparticle size and concentration on the rheology of ethylene glycol based nanofluids containing nanoparticles of five different metal oxides is investigated. Particle mass concentrations ranged from 5 to 20 wt %. Types of the nanoparticles and their particle size are TiO2 (30 nm, 50 nm), MgO (20 nm, 40 nm), ZnO (10-30 nm, 35-45 nm, 80-200 nm), SiO2 (20-30 nm, 60-70 nm) and CuO (40 nm, 80 nm). A stress controlled rheometer fitted with a cone-and-plate system is employed for the rheological characterization of the nanodispersions at temperatures between -5 degrees C and 35 degrees C. The non-linear measurements reveal that nanofluids of CuO (40 nm), ZnO (10-30 nm, 35-45 nm) and MgO (20 nm, 40 nm) particles exhibit non-Newtonian shear thinning behavior at particle mass concentrations higher than 5 %. No appreciable shear thinning is observed for the dispersions of TiO2 (30 nm, 50 nm) and SiO2 (20-30 nm, 60-70 nm) particles. Strong dependency between relative viscosity of the suspensions and particle size and loading is observed. Temperature, on the other hand, plays a marginal role in the relative viscosity of the suspensions. The shear viscosity measurements indicated the presence of particle size and concentration dependent apparent yield stress for CuO and ZnO nanofluids. Investigated nanofluids do not exhibit any thixotropy during their rheological characterization. Finally, viscoelastic measurements suggest that nanofluids are free of gel formation.