This paper deals with the global asymptotic stability (GAS) of certain nonlinear RLC circuit systems using the direct Lyapunov method. For each system a suitable Lyapunov function or energy-like function is constructed and the direct Lyapunov method is applied to the related system. Then the invariant equilibrium point of each system that makes the system solution to the global asymptotic stable is determined. Some new explicit GAS conditions of certain nonlinear RLC circuit systems are derived by Lyapunov's direct method. The presented simulations are compatible with the new results. The results are given with proofs.