Accurately predicting the impacts of climate change on hydrological fluxes in ungauged basins continues to be a complex task. In this study, we investigated the transferability of the model parameters SCS-SMA-LR, available in the ATHYS platform, to simulate hydrological behavior within catchments of a large South Mediterranean transboundary basin, i.e., the Medjerda bordering Tunisia and Algeria, characterized by contrasting climatic and physiographic conditions. A robustness analysis was set up for donor and receptor catchments situated in the Medjerda catchment in Tunisia. The model was initially calibrated for two donor catchments, for the 127 km2 catchment of the Lakhmess watershed situated on the right bank and for the 362 km2 catchment of the Raghay watershed situated on the left bank of the Medjerda basin in Tunisia, using input data from 1990 to 1994. The model performance was evaluated through multiple accuracy criteria based on the Best Linear Unbiased Estimator (BLUE) for the automatic calibration to quantify the model simulation, proving its good performance. The temporal transferability was assessed by evaluating model performance, transferring the calibrated parameters for the two catchments as validation on data for 3-year periods outside the calibration domain to test the robustness of the model through a diachronic analysis from different decades, i.e., for the periods 1994–1997, 2001–2004, and 2014–2017, respectively. The spatial transferability was assessed by transferring the parameters calibrated on the donor catchments to be applied to the receptor catchments based on similarity and data availability. The model was upgraded to a greater catchment for data from 1994 to 2016 for the right bank, the Siliana Upstream catchment, and to the nearest catchment with a similar area for the data from 2008 to 2017 for the left bank of the Medjerda basin, the Bouheurtma catchment. The capacity of the soil reservoir and the flow velocity parameters proved to have an important impact on the modeling implementations at, respectively, 123.03 mm and 1 m/s for Raghay, and 95.05 mm and 2.5 m/s for Lakhmes. The results show that the space–time transfer process of model parameters produces an acceptable simulation of flow volumes and timing. The proposed methodology proved to be a successful way to monitor ungauged catchments and strengthens the robustness of the SCS-SMA-LR model for hydrological modeling and impact studies in ungauged basins of the Southern Mediterranean region.