This work describes the building of an equivalent model of the Argentinian power system to be used in the study of dynamical phenomena of the Uruguayan system. By following the slow coherency methodology, the generators that oscillate coherently at the lowest natural frequencies of the interconnected system were identified with the help of the respective mode shapes. The corresponding linear model was built with second order classical generators models. In a second step, the coherent generators were clustered at the level of their internal nodes, building in this way the corresponding inertial equivalents. Finally, the system was reduced again with the help of classical linear techniques for the computation of static equivalents. The final result is an equivalent model of the Argentinian system that includes approximately 20% of the original machines and less than 5% of its nodes. The equivalent model was validated through the comparison of the transient response of the Uruguayan system to a set of significant faults.