Model suspensions with different concentrations of the rheological additives Aerosil 380 in silicone oil M20 000 and Bentone 27 in epoxy resin Araldite GY260 were researched. The shear stress and the first normal stress difference were measured simultaneously with shear flow start-up experiments followed by stress relaxation. At higher concentrations, the rheological additives build a strong three-dimensional (3D) structure that leads to systems with plastic flow behavior. It was established that the structure of 7.5% Aerosil 380 in silicone oil M20 000 is strong and stiff due to the big difference between shear stress and normal stress at small shear rates. This solid-like system exhibits only one yield stress region. It was found that the suspensions with a strong 3D structure and comparable values of shear stress and first normal stress difference at small shear rates have a first and a so-called second yield stress regions. In the transition section, between the two yield stress regions, there occurs a break of the distortion and a rearrangement of the structure. The decrease and increase of the first normal stress difference also belongs to the rearrangement of the structure. POLYM. ENG. SCI., 50:811-818, 2010. (C) 2009 Society of Plastics Engineers