The turbulence structure of flows of clay suspensions in smooth-boundary open channels were experimentally studied. Clay suspensions are non-Newtonian fluids. Transition from laminar to turbulent flows occurs when a Reynolds number Remis between 2,000 and 10.000. Three layers can be identified in transitional flows, i.e. a) laminar sublayer, b) turbulent layer, and c) upper layer. In the upper layer the turbulence intensity is low or even equal to zero. The flow between the turbulent layer and the laminar sublayer is alternatively laminar and turbulent. For various concentrations of clay suspension the mean velocity profiles follow the Coles' velocity formula with negative wake parameter and smaller Karman constant. The distribution of turbulence intensity is far more nonuniform than that of water flow. The probability density and autocorrelation coefficient are discussed and it is concluded that the turbulence in the non-Newtonian flow is produced in the turbulent layer and high frequency turbulence is suppressed by the high viscosity and yield stress.