Well-developed karst aquifers consist of highly conductive conduits and a relatively low permeability fractured and/or porous rock matrix and therefore behave as a dual-hydraulic system. Groundwater flow within highly permeable strata is rapid and transient and depends on local flow conditions, i.e., pressurized or nonpressurized flow. The characterization of karst aquifers is a necessary and challenging task because information about hydraulic and spatial conduit properties is poorly defined or unknown. To investigate karst aquifers, hydraulic stresses such as large recharge events can be simulated with hybrid (coupled discrete continuum) models. Since existing hybrid models are simplifications of the system dynamics, a new karst model (ModBraC) is presented that accounts for unsteady and nonuniform discrete flow in variably saturated conduits employing the Saint-Venant equations. Model performance tests indicate that ModBraC is able to simulate (1) unsteady and nonuniform flow in variably filled conduits, (2) draining and refilling of conduits with stable transition between free-surface and pressurized flow and correct storage representation, (3) water exchange between matrix and variably filled conduits, and (4) discharge routing through branched and intermeshed conduit networks. Subsequently, ModBraC is applied to an idealized catchment to investigate the significance of free-surface flow representation. A parameter study is conducted with two different initial conditions: (1) pressurized flow and (2) free-surface flow. If free-surface flow prevails, the systems is characterized by (1) a time lag for signal transmission, (2) a typical spring discharge pattern representing the transition from pressurized to free-surface flow, and (3) a reduced conduit-matrix interaction during free-surface flow. Copyright 2011 by the American Geophysical Union.