The Gershgorin Circles Theorem (GCT) is a very useful tool to characterize the regions of the complex plane in which the eigenvalues of a matrix are found. Within the analysis of local stability to equilibrium solutionx of a system of ordinary differential equations is vital to determine the sign of the real part of the eigenvalues of the Jacobian matrix evaluated inx. For this reason, a local stability test is formulated for equilibrium solutions, based on the indirect method of Lyapunov and GCT.