We have analysed Optical Gravitational Lensing Experiment photometry for first overtone classical Cepheids in the Large and Small Magellanic Clouds in search for additional periodicities beyond radial modes. We have used standard consecutive pre-whitening technique in some cases followed by time-dependent pre-whitening. We report new candidates for double-mode radial pulsations. However, majority of signals we have detected cannot be interpreted in terms of radial modes. We report 516 double-periodic stars with period ratios, P x/ P 1O, in the range 0.60–0.65. We study the properties of this class and implications for model explaining these periodicities. We also report 28 stars in which additional variability is of longer period, below radial fundamental mode, with median period ratio, P 1O/ P x, of 0.684. This class is an analogue of a class known in RR Lyrae stars. Hundreds of other signals were detected that cannot be attributed to radial modes or the above-mentioned classes. Statistical properties of these signals are analysed. We suggest that majority of these signals correspond to non-radial modes. In particular, a significant fraction can be attributed to non-radial modes of moderate degrees, tightly connected to a class with period ratios in between 0.60 and 0.65. In tens of stars, close to radial mode frequency, relatively large-amplitude and coherent signals are observed, which may represent yet another class. In 27 stars periodic modulation of pulsation was detected. Differences in additional frequency content between the two Clouds are discussed. [ABSTRACT FROM AUTHOR]