The steady‐state viscosities η and first normal stress differencesN1as functions of the shear rate γ̇ are measured for highly concentrated and densely packed solutions and melts of hydroxypropylcellulose (HPC) and a polyester [OQO(OEt)10] made from the condensation of 1,10‐decane‐bis‐benzoyl chloride and ethoxy substituted hydroquinone. As the concentration of HPC is increased, systematic departures from the predictions of the Doi theory are found. First, beginning at a concentrationCof around 30% by weight, the zero‐shear viscosity begins to increase, rather than decrease, with increasing concentration. Then, at a concentration of 35%, the shear rate γ̇maxat whichN1reaches a local maximum begins to decrease, rather than increase, with concentration, the viscoelastic activation energy of the solution begins to exceed that of the solvent, and the shape of the curve ofN1versus shear rate begins to become temperature sensitive. At a concentration of 55% at room temperature, the region of negativeN1disappears, although a local minimum ofN1remains. Finally, for bulk samples of HPC at elevated temperatures and for 60% solutions and bulk samples of [OQO(OEt)10],N1is positive only, with no local minimum. We hypothesize that this progressive breakdown in the predictions of the Doi theory as concentration increases is caused by polymer–polymer hindrances to translational motion that at high concentration can only be relieved by increasing the temperature and thereby increasing the flexibility of the molecules.