Suspensions of fumed silica in polypropylene glycol exhibit shear-thickening under steady shear and "strain-thickening" under oscillatory shear. Strain-thickening refers to a sharp increase in the complex viscosity eta* observed at critical combinations of strain-amplitude and frequency. Two regimes of strain-thickening behavior have been found : The first occurs at high critical strains and low frequencies, whereas the second occurs at high critical frequencies and a constant lower strain. Strain-thickening in the first regime can be explicitly correlated with steady shear-thickening, using a modified version of the Cox-Merz rule. Accordingly, strain-thickening data for the complex viscosity eta* as a function of the maximum dynamic shear-rate gamma(0) omega can be superposed against shear-thickening data for the steady viscosity as a function of the steady shear rate. Such a correlation between the two kinds of thickening phenomena has not been reported previously. The combination of shear- and strain-thickening behavior can be qualitatively explained using a clustering mechanism, which attributes the various phenomena to the formation of temporary, flow-induced clusters. The two regimes of strain-thickening are a result of differences in the relative ease of cluster formation.