Asteroseismology of Cepheids

The importance of Cepheids is well known in many fields of astronomy. In this contribution I would like to show how it is possible to obtain indications about the internal structure of a Cepheid and how we can test models of this class of variable stars. Section 2 introduces the Fourier decomposition, a tool to describe quantitatively the light curves of pulsating stars. In the past years I have been involved in a project concerning Cepheids with P < 8 d and in Sect. 3 I will show how an observational result was progressively built on the basis of old and new data; the latter were collected on selected targets just to clarify some controversial points. Since different pulsation modes were suspected among these stars, an independent confirmation was searched for. To do that we applied the least–squares technique to Double Mode Cepheids. By obtaining a very satisfactory description of their pulsational content (Sect. 4), we demonstrated how powerful the method is. Moreover, we could confirm that between Cepheids with P < 8 d they are both fundamental and first overtone pulsators (Sect. 5). The detection of small amplitude cross–coupling terms and higher harmonics in the light curves of Double Mode Cepheids allowed us to quantify the properties of the high– order terms and hence to discover other peculiarities (Sect. 6), very useful to complete the scenario of the resonance effects and to test some theoretical models (Sect. 7).