Linear and nonlinear viscoelastic properties were examined for a 50 wt % suspension of spherical silica particles (with radius of 40 nm) in a viscous medium, 2.27/1 (wt/wt) ethylene glycol/glycerol mixture. The effective volume fraction of the particles evaluated from zero-shear viscosities of the suspension and medium was 0.53. At a quiescent state the particles had a liquid-like, isotropic spatial distribution in the medium. Dynamic moduli G* obtained for small oscillatory strain (in the linear viscoelastic regime) exhibited a relaxation process that reflected the equilibrium Brownian motion of those particles. In the stress relaxation experiments, the linear relaxation modulus G(t) was obtained for small step strain gamma(less than or equal to 0.2) while the nonlinear relaxation modulus G(t, gamma) characterizing strong stress damping behavior was obtained for large gamma(> 0.2). G(t, gamma) obeyed the time-strain separability at long time scales, and the damping function h(gamma) (= G(t, gamma)/G (t)) was determined. Steady flow measurements revealed shear-thinning of the steady state viscosity eta(gamma) for small shear rates gamma (< tau(-1); tau = linear viscoelastic relaxation time) and shear-thickening for larger gamma (> tau(-1)). Corresponding changes were observed also for the viscosity growth and decay functions on start up and cessation of flow, eta(+) (t, gamma) and eta(-) (t, gamma). In the shear-thinning regime, the gamma and t dependence of eta(+) (t, gamma) and eta(-) (t, gamma) as well as the gamma dependence of eta(gamma) were well described by a BKZ-type constitutive equation using the G (t) and h (gamma) data. On the other hand, this equation completely failed in describing the behavior in the shear-thickening regime. These applicabilities of the BKZ equation were utilized to discuss the shear-thinning and shear-thickening mechanisms in relation to shear effects on the structure (spatial distribution) and motion of the suspended particles.