  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.
