This dissertation presents two theoretical predictions of the behavior of solutions of nematic liquid crystal polymers when subjected to small amplitude flows that are oscillatory in time. First, we review theoretical models for predicting the behavior of nematic liquid crystals, including Leslie-Ericksen theory, which only attempts to capture the mean direction of molecular orientation, and Doi-Hess kinetic theory, which defines a probability density function on the unit sphere for the molecular orientation and also the mesocscopic orientation tensor models derived from it, which are the models that we will examine. In Chapter 2, we examine shear flow in the monodomain limit, in which there are no spatial gradients in molecular orientation, and we use multiple timescale perturbation analysis to capture very slowly developing effects in the dynamic moduli, similar to experimental observations. Then, in Chapter 3, we relax the monodomain restriction and examine the effect of heterogeneity in the molecular orientation and the choice of two special anchoring conditions for the orientation at the plates. We re- cover a Leslie-Ericksen-type prediction, formally connect imposed stress and imposed velocity boundary conditions in shear flow, and establish an equivalence at the level of the storage and loss moduli between shear flow and Poiseuille flow
