Our previous experiments on the dynamics of laminar premixed flames on a circular porous plug burner have revealed periodic modes with different spatial and temporal characteristics. In this paper representative examples of nonperiodic modes will be presented, and it will be argued that these modes fall into two distinct classes. The method of data analysis used to make this identification will be explained and the experimental conditions that are conducive to observing the flame as a dynamical system will be described in detail. Our results suggest that the techniques of nonlinear dynamics are useful in classifying the periodic and chaotic modes of pulsating and cellular premixed flames but are probably not relevant to diffusion flames.