The first normal-stress difference N-1((gamma) over dot) and the shear viscosity eta((gamma) over dot) have been measured for liquid crystalline solutions of HPC in acetic acid (AA) as functions of the shear rate ((gamma) over dot) and the molecular mass of HPC. The measurements were done over four decades in, for two samples of HPC with M-W = 60,000 and 100,000 (Klucel E and L, respectively) and solution concentration c = 37% (c > c*). N-1((gamma) over dot) is observed to change from positive to negative and again to positive, as the shear rate ((gamma) over dot) increases. The ((gamma) over dot) values at which N-1 changes sign depend on M-W. The viscosity eta((gamma) over dot) Shows a small Newtonian plateau at low shear rates and a strong shear-thinning at higher values of ((gamma) over dot), including an "hesitation" similar to one previously observed in LC solutions of PBLG [2]. All these observations are rationalized within the framework of the constitutive equations for liquid crystalline polymers recently proposed by one of us [1]. Expressions for eta((gamma) over dot) and N-1((gamma) over dot) derived from this theory fit very well (quantitatively) to the experimental data and some fundamental viscoelastic parameters of the system are thereby obtained for the first time.