We have analysed high-precision photometry of 77 double-mode RR Lyrae (RRd) stars observed by NASA's Kepler-K2 mission during Campaigns 1-18. Among those stars, we have identified several low-period ratio variables, belonging either to a subclass of "anomalous" RRd stars (Soszy��ski et al., 2016) or to a separate shorter-period subclass recently identified by Prudil et al. (2017). A non-radial mode with the period ratio of $P_{\rm x}/P_{\rm 1} \sim 0.615$ has been detected in most RRd stars of our sample. In majority of these variables, at least one subharmonic of the non-radial frequency is also present. Our findings indicate that excitation of the non-radial mode is a common property of the RRd stars. The same non-radial pulsation is also commonly detected in the RRc stars. We show that properties of this puzzling mode are essentially the same in both groups of RR Lyrae-type pulsators.

Proceedings of "Physics of Oscillating Stars" (PHOST) conference, Banyuls-sur-mer, France, 2-7 September 2018