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We analyzed photometry for the up-to-date collection of the first-overtone RRLyrae stars (RRc; 11415 stars) and double-mode RR Lyrae stars (RRd; 148 stars)towards the Galactic bulge from the Optical Gravitational Lensing Experiment.We analyzed frequency spectra of these stars in search for additional,low-amplitude signals, beyond the radial modes. We focused on stars from twogroups: $RR_{0.61}$ and $RR_{0.68}$. In the first group, additionallow-amplitude signals have periods shorter than the first-overtone period;period ratios fall in the 0.60-0.64 range. In the second group, additionallow-amplitude signals have periods longer than the first-overtone period;period ratios tightly cluster around 0.68. Altogether we have detected 960 and147 RR Lyrae stars that belong to $RR_{0.61}$ and $RR_{0.68}$ groups,respectively, which yield the incidence rates of 8.3 and 1.3 per cent of theconsidered sample. We discuss statistical properties of RR Lyrae stars withadditional periodicities. For $RR_{0.61}$ group we provide strong argumentsthat additional periodicities are connected to non-radial pulsation modes ofdegrees $\ell=8$ and $\ell=9$, as proposed by Dziembowski. We have alsodetected two double-periodic variables, with two close periodicities, similarto RR Lyrae variable V37 in NGC 6362. Properties of these peculiar variables,which may form a new group of double-mode pulsators, are discussed.

The census of non-radial pulsation in first-overtone RR Lyrae stars of the OGLE Galactic bulge collection