The anomalous behavior of the (zero frequency) shear viscosity of colloidal systems on approach of the gas-liquid critical point is analyzed. As a result of hydrodynamic interactions, the anomalous behavior is found to be qualitatively different from that of molecular systems. On the basis of the asymptotic solution of the Smoluchowski equation for the shear rate dependent pair-correlation function, an expression for the non-Newtonian zero frequency viscosity of a near-critical suspension is derived. The viscosity depends on two dimensionless groups : on xi(-1) d via a cutoff function and on lambda alpha gamma xi(4) via the structurefactor (xi is the correlation length in the equilibrium system, d is the core diameter, and gamma is the shear rate). The transition from weak to strong shear occurs at lambda approximate to 1. The anomalous behavior of both the zero shear viscosity and the non-Newtonian characteristics is formally due to the fact that close to the critical point, where xi is large, a very small shear rate gamma is sufficient to make lambda a large number. The critical exponent for the zero shear viscosity is found to be equal to that of the correlation length. This exponent is much larger than for molecular systems, which is known to be very small (approximate to 0.03). The exponential behavior sets in at xi/d approximate to 3.