The rheological behavior of ethylene glycol-based nanofluids containing exfoliated graphite nanoplatelets has been carried out using a cone-plate Physica MCR rheometer. Initial experiments based on flow curves were carried out, the flow curves were based on the controlled shear stress model, these tests show that the studied nanofluids present non-Newtonian shear thinning behavior with yield stress. Furthermore, linear viscoelastic experiments were conducted in order to determine the viscoelastic behavior: using strain sweep and frequency sweep tests the storage and loss modulus were determined. The fractal dimension (Df) was estimated from the suspension static yield-stress and volume fraction (ϕ) dependence, and was determined to be Df = 2.36, a value consistent with a process of aggregation of RLCA type (reaction limited cluster aggregation). This value is unusual if compared with other nanofluids, and can be regarded as a result of the bidimensionality of the suspended nanoplatelets. Finally, creep-recovery tests and mechanical models confirm the viscoplastic nature of our nanofluids, a feature never shown so far for this type of systems, increasing the solid-like character in the range of concentrations studied if compared with other nanofluids reported in the literature. This is a result of the combination of a remarkable internal structure and strong interactions, which evidence an unexpected behaviour sharing many solid-like features.