The rheological, thermodynamic, and structural behavior of linear and branched alkanes in simple shear is investigated using nonequilibrium molecular-dynamics simulation of united atom model fluids. Our results for the zero-shear viscosity of pure linear alkanes as well as mixtures of alkanes are in reasonable agreement with experiment. Simulation results for intermediate molecular weight linear alkanes indicate that the simple models employed here are capable of describing the pressure and temperature dependence of the viscosity. More importantly, our calculations indicate that addition of short, flexible branches to alkanes leads to a viscosity enhancement of a factor of 2 or more, thereby offering interesting possibilities for formulation of lubricants with specific properties.