We investigate the rheological properties of a Landau-Ginzburg model that has competing interaction terms. These interactions have earlier been shown to produce mesoscopic ordering and such models have been helpful in explaining microemulsion behavior. Our present study is based on time-dependent Landau-Ginzburg equations for the order parameter and velocity field. The possible influence of hydrodynamic fluctuations, though discussed, is neglected in our treatment. General expressions for the excess viscosity and the first normal stress coefficient are derived in terms of the quasistatic structure factor. For steady shear flows and in the mean field approximation, explicit relations are given in two space dimensions for a nonconserved order parameter and in three space dimensions for a conserved order parameter, The former case is the easiest one to study numerically in computer simulations, Our numerical results show that mean field theory for the excess viscosity is satisfactory at some distance from the "transition" curve to the lamellar phase. The normal stress coefficient turns out to be very small. It only becomes appreciable close to the phase boundary. Here the nonlinear dependencies of excess viscosity and stress coefficient on the shear rate become important. To explain the general behavior we have considered terms up to fourth order in the shear rate. Computer simulations as well as mean field theory indicate that the quadratic corrections to both coefficients are negative in the microemulsion region. With increasing shear rate one therefore first enters a regime of shear-thinning. The quartic corrections are found to be positive, so further increase of the shear rate will lead to shear-thickening.