  We show how Principal Component Analysis can be used to analyse the structure
of Cepheid light curves. This method is more efficient than Fourier analysis at
bringing out changes in light curve shape as a function of period. Using this
technique, we study the shape of fundamental and first overtone mode Cepheid
light curves in the Galaxy, LMC and SMC over a wide period range. For
fundamentals, we find evidence for structural changes at $\log P \approx 1.55,
2.1$. It is suggested that the feature at $\log P \approx 2.1$ is associated
with a resonance in the Cepheid normal mode spectrum. For overtones, we recover
the Z shape in the $R_{21}$ period plane and reproduce the metallicity
dependence of this Z shape.
