We have modeled flow and dissolution processes within percolation networks representing stochastic primary fracture systems in limestone. At the beginning of karstification, flow is evenly distributed on all fractures available. As the system develops by dissolutional widening of the fractures, preferred flow pathways evolve, which attract more and more flow, until at breakthrough the total flow rate increases dramatically. These breakthrough times have been investigated with regard to their dependence on the initial fracture aperture width, the dimension of the evolving karst aquifer, hydraulic gradients, connectivity of the percolation network, and the chemical parameters, such as higher-order rate constants and exponents, and equilibrium concentration. They exhibit a behavior similar to that of breakthrough times for one-dimensional conduits <Dreybrodt, 1996>. Our results show that the structure of the evolving karst aquifer is determined by the initial geological setting. However, the final conduits are selected from competing pathways with potential breakthrough times close to each other whereby the details of the distribution of undersaturation with respect to calcite play an important role. ¿ 1998 American Geophysical Union