  A new, extended time-series photometry of M3 RR Lyrae stars has revealed that
four of the ten double-mode stars show large-amplitude Blazhko modulation of
both radial modes. The first, detailed analysis of the peculiar behavior of the
unique, Blazhko RRd stars is given. While the P1/P0 period ratio is normal, and
the overtone mode is dominant in the other RRd stars of the cluster, the period
ratio is anomalous and the fundamental mode has a larger (or similar) mean
amplitude than the overtone has in Blazhko RRd stars. The modulations of the
fundamental and overtone modes are synchronized only in one of the Blazhko RRd
stars. No evidence of any connection between the modulations of the modes in
the other three stars is found. The Blazhko modulation accounts, at least
partly, for the previously reported amplitude and period changes of these
stars. Contrary to the $\sim50$$%$ Blazhko statistics of RRab and RRd stars,
Blazhko modulation occurs only in 10$%$ of the overtone variables in M3. Four
of the five Blazhko RRc stars are bright, evolved objects, and one has a
similar period and brightness as Blazhko RRd stars have. The regions of the
instability strip with high and low occurrence rate of the Blazhko modulation
overlap with the regions populated by first- and second-generation stars
according to theoretical and observational studies, raising up the possibility
that the Blazhko modulation occurs preferentially in first-generation RR Lyrae
stars.
