We report on the rheological properties of water suspensions of poly(methacrylic acid-co-poly(ethylene oxide) methyl ether methacrylate)-b-polystyrene and poly(methacrylic acid-co-poly(ethylene oxide) methyl ether methacrylate)-b-poly(methyl methacrylate) self-assembled amphiphilic block copolymer nanofibers, synthesized via RAFT-mediated aqueous emulsion polymerization. The viscoelastic properties were studied over a range of nanofiber concentrations spanning the transition from the dilute to semidilute regimes. From the measured viscoelastic parameters, two sets of suspensions could be differentiated depending on their aspect ratio (length/diameter approximate to 70 and, approximate to 54) and the average length of the nanofibers was calculated in the 2.4 mu m - 3.8 mu m range. The viscoelastic properties appeared to depend mainly on the aspect ratio of the fibers rather than on their nature and composition. As expected the zero shear viscosity was observed to scale with the volume fraction phi as eta(0) proportional to phi(1) and eta(0) proportional to phi(3) for dilute and semidilute regime, respectively. However, the deviation of the scaling law in semidilute regime at higher concentrations and the slowdown of the rotary diffusion can be related to different mechanisms. While a Brownian motion of nanofibers is the dominant mechanism of relaxation, it was also concluded that clustering phenomenon and broad length distribution of nanofibers implies that some large nanofibers could be non Brownian.