Using room-temperature liquid metal particles as fillers in polymer composites (PCs) has recently been of utmost interest as the resultant composites exhibit improved toughness along with electrical and thermal conductivity. This paper presents a comprehensive study on shear and extensional rheology of the aqueous solutions (inks) of liquid EGaIn (eutectic gallium-indium) particle and poly(ethylene oxide)-based PCs. The rheology of this material system is compared to solid-state, rigid graphene-based PC inks having the same polymer matrix and filler concentrations. Results show that EGaIn-based PC inks exhibit unique rheological behavior that is inconsistent with that of the conventional rigid filler-based Polymer Nanocomposites (PNs), exemplified by increased extensional flow capability and elasticity. We postulate that the source of this behavior is the elastic nature of the oxide covered EGaIn particles. EGaIn-based PCs eliminate common trade-offs for conductive PCs and thus can have a significant impact in several technologies including solid-state energy storage and 3D-printing. (C) 2019 The Society of Rheology.