The OGLE project led to discovery of earlier unknown forms of multiperiodic pulsation in Cepheids. Often, the observed periods may be explained in terms of simultaneous excitation of two or rarely three radial modes. However, a secondary variability at about 0.6 of the dominant period, detected in a number of the first overtone (1O) pulsators inhabiting the Magellanic Clouds, seems to require a different explanation. After reviewing a possibility of explaining this signal in terms of radial and nonradial modes, I find that only unstable modes that may reproduce the observed period ratio are f-modes of high angular degrees (l=42-50). I discuss in detail the driving effect behind the instability and show that it is not the familiar opacity mechanism. Finally, I emphasize the main difficulty of this explanation, which requires high intrinsic amplitudes implying large broadening of spectral line.
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