The theory of transport in highly inhomogeneous systems, developed recently by Pozhar and Gubbins, and the nonequilibrium molecular dynamics (NEMD) technique are employed to study the viscosity of WCA fluids cofined in narrow slit pores of width 5.1 and 20 sigma at reduced densities rho sigma(3) of 0.422-0.713. Calculated quantities include the equilibrium and nonequilibrium density profiles, equilibrium pair correlation functions, how velocity profiles, and the viscosity profiles. NEMD simulation results are compared with the theoretical predictions. The agreement is good except for the region within one molecular diameter from the walls. The viscosity was found to vary with position across the pore.