Starting from a nonlocal description of the stress in a slender, rigid fiber:suspension [Schiek and Shaqfeh (1995)], we calculate the dynamic properties of a free-fiber suspension under oscillatory shear ina very narrow gap. For a fiber suspension, three held quantities including the fluid velocity, the fiber concentration, and the fiber configuration strongly affect the suspension’s behavior. When the width of the gap confining the suspension is of the same scale as a suspended fiber’s length, then all three of the important field quantities change rapidly on that scale. The nonlocal stress equation is coupled to the momentum conservation equation for the fluid velocity and a Fokker-Plank equation for the fiber’s probability density function resulting in a closed set of nonlinear, integrodifferential equations. These equations were solved in the limit of a small Peclet number, where Brownian motion dominates, for arbitrary gap widths and oscillation frequencies. From the calculated stress fields, we : obtained the real and imaginary viscosities that one would measure in flow experiments. The dependence of all four dynamic properties on gap width was investigated and we find that below a critical gap width (equivalent to one full fiber length) all dynamic properties undergo dramatic changes. Additionally, as the gap width shrinks, the relaxation time of the suspension was found to decrease, approaching the relaxation time of the pure Newtonian solvent in the limit of zero gap width. Scalings for the relaxation time as a function of small gap width are also presented.