This paper examines the effects of steady-state and transient hydrogen enrichment on thermoacoustic instability in a model gas turbine combustor. Combustion instability, a feedback loop between flame heat release rate oscillations and combustor acoustics, is characterized in a swirl-stabilized flame operated at a range of hydrogen-natural gas fuel blends and heat rates. Measurements of combustor chamber pressure fluctuations and CH* chemiluminescence imaging are used to characterize instability at a range of operating conditions. Steady-state tests show that both mixture heat rate and hydrogen content affect system stability. At a given heat rate, higher levels of hydrogen result in unstable combustion. As heat rate increases, instability occurs at lower concentrations of hydrogen in the fuel. Transient operation was tested in two directions – instability onset and decay – and two hydrogen-addition times – a short time of 1 millisecond and a longer time of 4 seconds. Results show that instability onset processes, through the transient addition of hydrogen, are highly repeatable regardless of the timescale of hydrogen addition. Certain instability decay processes are less repeatable, resulting in cases that do not fully transition from unstable to stable combustion despite similar changes in hydrogen fuel flow rate. Flame behavior before, during, and after the transient is characterized using high-speed CH* chemiluminescence imaging. Analysis of the high-speed images show changes in flame stabilization and dynamics during the onset and decay processes. The results of this study can have implications for systems that experience variations in fuel composition, particularly in light of growing interest in hydrogen as a renewable fuel.