We demonstrate, to the best of our knowledge, the first carrier-envelope offset (CEO) frequency stabilization of a GHz femtosecond laser based on opto-optical modulation (OOM) of a semiconductor saturable absorber mirror (SESAM). The 1.05-GHz laser is based on a Yb:CALGO gain crystal and emits sub-100-fs pulses with 2.1-W average power at a center wavelength of 1055 nm. The SESAM plays two key roles: it starts and stabilizes the mode-locking operation and is simultaneously used as an actuator to control the CEO frequency. This second functionality is implemented by pumping the SESAM with a continuous-wave 980-nm laser diode in order to slightly modify its nonlinear reflectivity. We use the standard f -to-2f method for detection of the CEO frequency, which is stabilized by applying a feedback signal to the current of the SESAM pump diode. We compare the SESAM-OOM stabilization with the traditional method of gain modulation via control of the pump power of the Yb:CALGO gain crystal. While the bandwidth for gain modulation is intrinsically limited to ∼250 kHz by the laser cavity dynamics, we show that the OOM provides a feedback bandwidth above 500 kHz. Hence, we were able to obtain a residual integrated phase noise of 430 mrad for the stabilized CEO beat, which represents an improvement of more than 30% compared to gain modulation stabilization. Optical frequency combs from mode-locked lasers [1-3] constitute a versatile tool for various applications such as optical frequency metrology [4,5], atomic clocks [6,7], or broadband high-resolution spectroscopy [8,9]. Some applications, e.g., the generation of ultra-low phase noise microwave signals by optical-to-microwave frequency division [10,11] or the calibration of astronomical spectrographs [12,13], benefit from the use of frequency combs with a high repetition rate in the multi-GHz range owing to their high power per comb mode and ease of access to individual optical lines. Most applications also require full-frequency comb stabilization, i.e., the two degrees of freedom, the repetition rate f rep , and the carrier-envelope offset (CEO) frequency f CEO need to be phase-coherently stabilized. The phase-stabilization of the CEO beat is usually the most challenging part. Since the CEO noise intrinsically scales with the repetition rate [14], the challenge is particularly pronounced for GHz repetition rate lasers. Traditionally, CEO stabilization is achieved using a phase-locked loop with feedback applied to the pump power of the femtosecond laser after detection of the CEO beat using nonlinear f-to-2f interferometry [1]. This method is particularly suitable for diode-pumped femtosecond lasers, such as fiber lasers or diode-pumped solidstate lasers (DPSSLs), for which the injection current of the pump diode can be directly modulated. However, the stabilization bandwidth is fairly limited by the cavity dynamics. The latter is partially determined by the upper-state lifetime of the gain material, which is typically in the range of a few μs to a few ms for the most comm...