The concept of a network motif-a small set of interacting genes which produce a predictable behaviour at the network level-has attracted considerable attention amongst network analysts. It is of particular interest to synthetic biology, a new discipline which aims to apply engineering principles to biological systems. The modular nature of network motifs would make them ideal candidates for the basic components of an engineered organism. In this paper we investigate the relationship between the presence of network motifs and oscillatory dynamics in a yeast transcriptional network and a set of computational networks, evolved to exhibit oscillatory behaviour. Our results do not support the hypothesis that network motifs are critical to network dynamics, possibly because they are tightly connected to many other components of the complex cell-wide transcriptional network.