AconstitutiveequationtheoryofOldroydfluidBtype,i.e.theco-rotationalderivativetype,isdevelopedfortheanisotropic-viscoelasticfluidofliquidcrystalline(LC)polymer.Analyzingtheinfluenceoftheorientationalmotiononthematerialbehaviorandneglectingtheinfluence,theconstitutiveequationisappliedtoasimplecaseforthehydrodynamicmotionwhentheorientationalcontributionisneglectedinitandtheanisotropicrelaxation,retardationtimesandanisotropicviscositiesareintroducedtodescribethemacroscopicbehavioroftheanisotropicLCpolymerfluid.UsingtheequationfortheshearflowofLCpolymerfluid,theanalyticalexpressionsoftheapparentviscosityandthenormalstressdifferencesaregivenwhichareinagoodagreementwiththeexperimentalresultsofBaeketal.Forthefiberspinningflowofthefluid,theanalyticalexpressionoftheextensionalviscosityisgiven.
