Semidilute mixtures of the cationically modified cellulose-based polyelectrolyte JR 400 and the anionic surfactant sodium dodecyl sulfate (SDS) form highly viscous solutions if a slight excess of charges from the polyelectrolyte is present. The reason for this is the formation of mixed rodlike aggregates in which the surfactant cross-links several polyelectrolyte chains. The same solutions also show shear-thinning behavior. In this paper, we use rheoSANS to investigate the structural evolution of the rodlike aggregates under steady shear and thereby elucidate the mechanism of shear-thinning in these viscous oppositely charged polyelectrolyte surfactant complexes.