The shear and extensional rheology of aqueous suspensions of cellulose nanofibrils (CNF) were investigated under dynamic and steady flow fields. The results were compared to those for two biopolymer solutions, cellulose acetate, CA, and guar gum, GG. Wet-spinning experiments were conducted for each system and the outcome related to the respective rheological profile. The spinnability of the system correlated with strong Newtonian and viscous responses under shear as well as long breakup time in capillary breakup experiments. CA solution was the most spinnable, also displaying the strongest Newtonian liquid behavior and the longest capillary breakup time. In contrast, the most shear-thinning and elastic CNF suspension showed instant capillary breakup and was considerably less spinnable. This is due to the limited entanglement between the rigid cellulose fibrils. In order to enable continuous wet-spinning of CNF without filament breakup, GG and CA were used as carrier components in coaxial spinning. The shear and extensional rheology of the system is discussed considering both as supporting polymers.