A methodology is presented for organizing experimental data and for qualitative modeling of complex dynamic behavior that can be described as due to two different periodic motions. When the experimental data are organized in a bifurcation map the nature of the bifurcation and organizing centers may be identified by a comparison with the dynamic features of a qualitative model having these different time scales. Phase space analysis of this three-variable model shows that its behavior can be determined from the bifurcation diagram of the two-variable model when the slowest variable is treated as a parameter. The two-variable bifurcation diagram can be constructed from the observed time traces. The analysis and modeling presented here are helpful in organizing experimental data, in classifying observed features, and for developing a mathematical model. These points are demonstrated by identifying and organizing observations of dynamic behavior in the chlorite-thiosulfate liquid-phase reaction (Epstein and Orban) and in acetaldehyde gas-phase oxidation (Gray et al.).