We report rheological studies of micellar nematic phases of potassium laurate/ decanol/ water mixtures with and without addition of salt (K2SO4) at a fixed temperature of 20 C-a similar to. Using a cone-plate rheometer, we verified that the ternary mixture (i.e., without salt) exhibiting the discotic (N (D) ) nematic phase showed only a slight pseudo-plastic (or shear-thinning) behavior. In contrast, a pronounced pseudo-plastic effect was observed in the N (D) phase of the quaternary samples. On the other hand, all the N (C) samples (salted or unsalted) showed a quasi-Newtonian behavior. In addition, we have made viscosity measurements using a (variation of a) rotating Couette flow viscometer. Finally, we also performed density measurements, using a density cell attached to the viscometer. Our results showed a contrasting behavior between the two types of nematic phases in two aspects. Firstly, regarding the ternary samples only, the apparent viscosity eta at moderate shear rates was lower in the N (C) than in the N (D) phase. The second aspect, regarding both ternary and quaternary samples, is that eta in the N (D) phase dramatically increased as the salt concentration increased, while in the N (C) phase eta was quite insensitive to the addition of salt. In order to analyse the results, we have used two different theoretical frameworks, namely the nematodynamics in the first aspect and the classical theory of electrolyte solutions in the second one.