The shear creep response of homeotropic monodomains of4,4′-n-octylcyanobiphenyl (8CB) and dilute solutions of a side-chain liquid-crystalline polysiloxane (LCP) inN-(4-methoxybenzylidene)- 4-butylaniline (MBBA) is studied in the absence and presence of electric fields applied along the director. In the absence of the field, oscillations in strain rate are observed for 8CB and the LCP/MBBA solutions, indicative of director-tumbling flow. In the presence of electric fields, the tumbling flow is suppressed and, with increasing field strength, a systematic evolution is observed toward flow-aligning, the apparent viscosity being determined by the balance in hydrodynamic and electric torques. Due to a larger dielectric anisotropy, the tumbling flow of 8CB is suppressed at a critical field strength much lower than that of the LCP/MBBA solution. Moreover, a field-induced asymmetry of the doublet peaks is observed in the creep deformation for 8CB at 34 °C. Based on Ericksen’s transversely isotropic fluid theory, simulation of the influence of electric fields on the flow-tumbling behavior is performed and qualitative agreement with the experimental results is obtained.