  We analyse photometry for 138 first overtone Cepheids from the Small
Magellanic Cloud, in which Optical Gravitational Lensing Experiment (OGLE) team
discovered additional variability with period shorter than first overtone
period, and period ratios in the (0.60, 0.65) range. In the Petersen diagram
these stars form three well separated sequences. The additional variability
cannot correspond to other radial mode. This form of pulsation is still
puzzling.
  We find that amplitude of the additional variability is small, typically 2-4
per cent of the first overtone amplitude, which corresponds to 2-5 mmag. In
some stars we find simultaneously two close periodicities corresponding to two
sequences in the Petersen diagram. The most important finding is the detection
of power excess at half the frequency of the additional variability (at
subharmonic) in 35 per cent of the analysed stars. Interestingly, power excess
at subharmonic frequency is detected mostly for stars of the middle sequence in
the Petersen diagram (74 per cent), incidence rate is much lower for stars of
the top sequence (31 per cent), and phenomenon is not detected for stars of the
bottom sequence. The amplitude and/or phase of the additional periodicities
strongly vary in time.
  Similar form of pulsation is observed in first overtone RR Lyrae stars. Our
results indicate that the nature and cause of this form of pulsation is the
same in the two groups of classical pulsators; consequently, a common model
explaining this form of pulsation should be searched for. Our results favour
the theory of the excitation of non-radial modes of angular degrees 7, 8 and 9,
proposed recently by Dziembowski.
