Oscillatory water levels in observation wells have commonly been recorded at the beginning of aquifer tests in highly transmissive fractured formations. In this paper, oscillatory water levels are predicted by the equations coupling the fluid movement in the observation well and the fluid movement in the surrounding formation. The equivalent-porous medium and dual-porosity models of fractured rock are two models considered in this analysis; however, other conceptual models of fractured media can also be coupled with the model presented here for fluid movement in the observation well. Type curves for the response of water levels in observation wells due to pumping in another well are generated by numerical inversion of the Laplace transform solution to the governing equations. Overdamped conditions, where inertial effects are insignificant, and underdamped conditions, where oscillations arise, are predicted by the solution to the governing equations. By matching water level measurements with the appropriate type curve, a conceptual model of the formation can be identified, and aquifer properties can be estimated. This analysis is applied in the interpretation of an aquifer test conducted in a fractured dolomite in northeastern Illinois. If the early time oscillations are ignored, the measured water levels can be explained by an equivalent-porous medium model. By analyzing the early time oscillations, however, the formation is shown to respond as a dual-porosity medium with a storativity of the fracture porosity that is an order of magnitude smaller than the storativity estimated from the equivalent-porous medium model.