The use of carbon nanotubes (CNTs) as a thickening agent in polyalphaolefin oils to create CNT-grease has significant merit. Given the abnormally high thermal conductivities of CNTs, it is conceivable that a CNT-grease would exhibit excellent thermal conductivity. The rheological response of CNT-greases is important for two reasons: to determine if the grease will have sufficient lubricating properties and to provide critical information on the structure and particle-particle interactions of CNT suspensions. The viscoelastic response and evidence of creep recovery support the theory of the stable 3 Dimensional network (3D) formation in the CNT-grease. The elastic response indicates that significant energy is needed to dismember the network structure and initiate viscous flow. The macroscopic rheological investigation provides additional information regarding the structure of CNT-grease and particle-particle interactions at high SWNT concentrations, ~10.0 wt. The knowledge gained concerning the structure of CNT suspensions will allow its manipulation to achieve better thermal properties.