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• A dye-based modeling approach was made for the first time in a Neoproterozoic karst hydrosystem. • Geo-speleological features association to develop conceptual models of karst systems. • Spatio-temporal resolutions of flow and transport parameters by equilibrium and non-equilibrium models. • Comparison of hydrodynamic behavior of recent karst systems with Neoproterozoic karst. Brazilian Neoproterozoic carbonate rocks, dating from about 740–590 million years ago, contain the oldest karst-structured terrains on Earth, resulting in groundwater flow pathways in highly heterogeneous and anisotropic conduit networks. Unlike Paleozoic and Mesozoic rocks, in Neoproterozoic karst systems, groundwater circulates and stores practically through dissolution features characterized as tertiary porosity, as the rock's primary porosity is recrystallized, considered negligible. However, studies using hydrodispersive equilibrium and non-equilibrium models to estimate flow and transport parameters to base the hydrodynamic behavior of these areas are not common. This paper proposes this, by a set of techniques involving dye tracer tests and the analysis of breakthrough tracer curves (BTCs) in a highly karstified Neoproterozoic terrain. For this, three karst springsheds, in the east, west, and south areas of the São Miguel river watershed, in Alto São Francisco karst region, Brazil, were choose and studied with dye tracer tests using Rhodamine WT and Uranine during dry and wet seasons, associated with regional/local (hydro)geological-structural, geomorphological, and speleological data. The results identified spatial and seasonal variations of water flow and transport parameters, recharge and discharge zones, and water dynamic and speleogenetic evolutions. BTCs models showed the karst systems are very dynamic with seasonal variations, and heterogeneities (bypass, loops and stagnant zones) control the variation of flow and transport parameters. The hydrodispersive parameters (mean flow velocity, and longitudinal dispersion coefficient) and coefficients of non-equilibrium models (partition, β, and mass transfer, ω) show a direct dependence on hydrogeological and speleogenetic contexts. Furthermore, the comparison with other karst systems around the world showed that Neoproterozoic karst has a more stable hydrodynamic behavior under hydrological conditions. [ABSTRACT FROM AUTHOR]