Oscillatory translational and rotational motions of small particles in viscous fluids are studied for two cases: (i) circular disks and (ii) nearly spherical particles. For circular disks, four motions are treated: broadside and edgewise oscillatory translations and out-of-plane and in-plane oscillatory rotations. In each case the unsteady Stokes equations are reduced to dual integral equations and solved exactly for all frequencies. Streamline portraits of the flow fields are used to understand the evolution of the velocity and pressure fields. The motions of nearly spherical particles are then studied using the reciprocal theorem. Asymptotic formulae for the hydrodynamic resistance tensors are derived and discussed.