  RR Lyrae stars are classical pulsating stars. They pulsate mostly in the
radial fundamental mode (RRab stars), in the radial first overtone mode (RRc
stars), or in both modes simultaneously (RRd stars). Collection of variable
stars from the Optical Gravitational Lensing Experiment (OGLE) contains more
than 38 000 RR Lyrae stars from the Galactic bulge. We analysed these data for
RRc and RRd stars. We have found new members of radial-non-radial double-mode
RR Lyrae stars, with characteristic period ratio of the two modes around 0.61.
We increased the number of known RR Lyrae stars of this type by a factor of 8.
We have also discovered another group of double-mode RR Lyrae stars. They
pulsate in the first overtone and in another, unidentified mode, which has
period longer than period of the undetected fundamental mode. The period ratios
tightly cluster around 0.686. These proceedings are focused on this puzzling
group. In particular, we report eight new members of the group.
