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 .