The onset of shear thickening (dilatancy) has been studied in submicron model suspensions of sterically stabilized spherical particles. Stress controlled rheometers have been used for this purpose, so that measurements can be performed beyond the onset of sudden shear thickening. Systematic data are presented for the effect of particle size, particle concentration, and the nature of the suspending medium on the onset of shear thickening. As a first approximation, the critical shear rate changes inversely proportional with the medium viscosity. The changing solvency of the medium for the stabilizer polymer introduces additional changes through effects on the thickness and stiffness of the steric barrier Thinner, stiffer barriers cause lower critical shear rates. In the softer systems the critical shear stress becomes independent of particle concentration in dense suspensions. This does not seem to be the case for the harder systems. The effect of particle radius a could shed some light on the underlying mechanisms of shear thickening. The data do not, however, enable us to decide between a scaling for the critical shear rate with a(2) or one with a(3). The latter seems more appropriate for harder systems, the former for softer ones.