The asymptotic structure of turbulent boundary layers of purely viscous non-Newtonian systems is investigated through the intermediate variable technique. The cases of power-law and Carreau fluids are discussed in detail. Results show that a classical two-layered structure persists, with a viscous layer thickness that is dependent on the power-law index, n, and a logarithmic solution in the fully turbulent region. For Carreau fluids, in general, a three-layered structure emerges, with two nested viscous sub-layers. Experimental and numerical data from other authors are used to determine the functional behaviour of the linear coefficient of the log-law with n. (C) 2013 Elsevier B.V. All rights reserved.