The theological behavior of dilute nematic mixtures containing liquid crystal polymers (LCP) with different molecular architectures dissolved in low molar mass nematogens is investigated. Addition of a side-chain LCP (MSHMA) to a flow-aligning nematic solvent, pentylcyanobiphenyl (5CB), alters the theology to director-tumbling character. Conversely, dissolution of a main-chain LCP (TPB-15) in a director-tumbling nematic, octylcyanobiphenyl (8CB), suppresses the tumbling behavior and produces a flow-aligning response. A characteristic pattern of shear stress oscillations is observed for MSHMA/5CB mixtures and pure 8CB, indicative of director tumbling, in flow startup, step flow, and flow reversal experiments. In contrast, TPB-15/8CB and TPB-15/5CB mixtures show no oscillatory response but a single stress overshoot, characteristic of a flow-aligning nematic such as pure 5CB. Concentration and temperature dependences of the theological effect of LCP are presented. Our results demonstrate that addition of sufficient amounts of LCP to a nematic solvent can change the sign of the Leslie viscosity coefficient alpha(3). Our findings are qualitatively consistent with a theoretical model of Brochard (1979), provided that the side-chain LCP has an oblate molecular configuration, while the main-chain LCP maintains a prolate molecular configuration in the nematic solvent. Analysis of the transient shear response function via the Erickson-Leslie-Parodi formalism yields viscosity coefficients of the mixtures and hence an estimate of the effective axial ratio of the polymer chain.