  We analyzed photometry for the up-to-date collection of the first-overtone RR
Lyrae 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 two
groups: $RR_{0.61}$ and $RR_{0.68}$. In the first group, additional
low-amplitude signals have periods shorter than the first-overtone period;
period ratios fall in the 0.60-0.64 range. In the second group, additional
low-amplitude signals have periods longer than the first-overtone period;
period ratios tightly cluster around 0.68. Altogether we have detected 960 and
147 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 the
considered sample. We discuss statistical properties of RR Lyrae stars with
additional periodicities. For $RR_{0.61}$ group we provide strong arguments
that additional periodicities are connected to non-radial pulsation modes of
degrees $\ell=8$ and $\ell=9$, as proposed by Dziembowski. We have also
detected two double-periodic variables, with two close periodicities, similar
to RR Lyrae variable V37 in NGC 6362. Properties of these peculiar variables,
which may form a new group of double-mode pulsators, are discussed.
