Co-evolutionary EAs are often applied to optimization and machine learning problems with disappointing results. One of the contributing factors to this is the complexity of the dynamics exhibited by co-evolutionary systems. In this paper we focus on a particular form of competitive co-evolutionary EA and study the dynamics of the fitness of the best individuals in the evolving populations. Our approach is to try to understand the characteristics of the fitness landscapes that produce particular kinds of fitness dynamics such as stable fixed points, stable cycles, and instability. In particular, we show how landscapes can be constructed that produce each of these dynamics. These landscapes are extremely similar when inspected with respect to traditional properties such as ruggedness / modality, yet they yield very different results. This shows there is a need for co-evolutionary specific analysis tools.