A premixed flat flame on a circular porous plug burner can form patterns of one or two concentric rings of cells in which brighter, hotter regions are separated by darker, cooler cusps and folds. Dynamic states are found at parameter values that are interleaved between those of the ordered states. Rotating states, modulated rotating states, hopping states, and intermittently ordered states have all been observed with motions of ∼100°/s. These states have been described using the ideas of dynamical systems. Their characteristics have been analyzed using modal decomposition techniques. Ratcheting states are qualitatively and quantitatively different from these other dynamic states. In ratcheting states one or both of the concentric rings rotate very slowly, ∼0.8°/s, each speeding up and slowing down in a manner unique to that state. Measurements of the angular displacement and computed values of the angular velocity are presented for four ratcheting states. The experimental results are discussed in the context of the physical characteristics of the flame front and in terms of bifurcations of systems with symmetry. Many of the principal features of ratcheting motion are not yet understood.