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The paper presents an in-depth investigation of the dynamic performance of the Static Synchronous Compensator (STATCOM) and the Static Synchronous Series Compensator (SSSC) theoretically and by exact digital simulation. A 24-pulse GTO dc-ac converter model is designed to represent the operation of the STATCOM and SSSC within a power transmission system. Two major factors of the STATCOM instability are analyzed and a new Automatic Gain Controller (AGC) is proposed to ensure the stable operation of the STATCOM under various load conditions. It is shown that the Phase-Locked Loop (PLL) inherent delay has a great effect on the dynamic operation of the SSSC and a new auxiliary regulator is proposed to enhance the dynamic performance of the SSSC. The proposed control schemes are validated by digital simulation.