The period-radius relation of classical Cepheids and the problem of their mode identification

Based on radial-velocity measurements and photometric observations, we calculated the radii of around 200 classical Cepheids that were previously assumed to be fundamental-mode pulsators. Our detailed analysis of the period-radius diagram shows that the sample of Cepheids with pulsation periods shorter than 9 days probably contains a significant fraction (up to 30%) of stars pulsating in the first overtone.