Mixtures of ionic liquid (IL) with poly(ethylene glycol) (PEG) may afford media with favorable properties. Dynamic viscosities of mixtures of a common and popular IL 1-butyl-3-methylimidazolium hexafluorophosphate ([bmim][PF(6)]) with PEGs of average molecular weight (MW) 200 (PEG200), average MW 400 (PEG400), number-average MW M(n) 570-630 (PEG600), and number-average MW M(n) 950-1050 (PEG1000) over a complete composition range at 10 degrees intervals in the temperature range of 10-90 degrees C are measured. The temperature dependence of the dynamic viscosity shows ([bmim][PF(6)] + PEG) mixtures to behave as Newtonian fluids and is found to follow Arrhenius-type behavior. In the IL-rich region, excess logarithmic viscosities for the ([bmim][PF(6)] + PEG200) mixture are found to be negative and independent of the temperature. Mixtures of ([bmim][PF(6)] + PEG600) and ([bmim][PF(6)] + PEG1000) show rare and unusual viscosity "synergism" or "hyperviscosity" in the sense that the mixture viscosity is observed to be significantly higher than the viscosity of both the neat components forming the mixture, giving rise to large positive excess logarithmic viscosities. These positive excess logarithmic viscosities decrease with increasing temperature. Formation of extensive H-bonding between the IL and PEG more than compensates for the losses in Coulombic attractive and van der Waals interactions within [bmim][PF(6)] and PEG600/PEG1000, respectively, giving rise to viscosity synergism. This compensation is not enough for ([bmim][PF(6)] + PEG200) and ([bmim][PF(6)] + PEG400) mixtures. The evidence for H-bonding in the mixtures is provided by FTIR absorbance data. The product of the monomer-to-excimer emission intensity ratio and the lifetime of the intramolecular excimer fluorescence of a microfluidity probe, 1,3-bis(1-pyrenyl)propane (BPP), is used as a reflection of the microviscosity of the mixture at different temperatures. The microviscosity shows synergistic effects in all four ([bmim][PF(6)] + PEG) mixtures. The contribution of H-bonding to the microviscosity reported by BPP is observed to be more then that as compared to contributions of Coulombic and van der Waals interactions. Synergism in the dynamic viscosity and microviscosity of ([bmim][PF(6)] + PEG) mixtures is a complex interplay of inter- and intramolecular H-bonding as well as Coulombic and van der Waals type interactions.