Combustion-induced instabilities are minimized in gas turbine combustors by incorporating one or more Helmholtz resonators into the combustor. First and second plates located in the head end of the combustor casing define one cavity, and a sleeve located between the casing and the liner defines another cavity. Each of the two cavities is connected to the combustion chamber by one or more throats, thus forming Helmholtz resonators. The throats of each resonator can be tubes of different lengths and/or different cross-sectional areas to provide dynamics suppression over a broad band of frequencies. The throats can also be arranged such that each throat is associated with a different portion of its respective cavity, each cavity portion having a different volume.