Our previous experiments have shown that cellular flames form ordered states consisting of concentric rings of cells. The numbers of cells in the inner and outer rings change independently in integer steps as the flow rate is increased. In this paper we report the observation of states characterized by a hopping motion in which cells abruptly change their angular position in the ring. This hopping proceeds sequentially to the other cells in the ring. The hopping states are typically observed in isobutane-air cellular flames at parameter values between those corresponding to two consecutive ordered states. The physical characteristics of these states are similar to those of modulated traveling waves found by Bayliss, Matkowsky and Riecke in numerical simulations of the full equations that describe the thermodiffusive instability. The similarities and differences between our experimental results and their theoretical predictions are discussed.