  Classical Cepheids (CCs) and RR Lyrae stars (RRLs) are important classes of
variable stars used as standard candles to estimate galactic and extragalactic
distances. Their multiplicity is imperfectly known, particularly for RRLs.
Astoundingly, to date only one RRL has convincingly been demonstrated to be a
binary, TU UMa, out of tens of thousands of known RRLs. Our aim is to detect
the binary and multiple stars present in a sample of Milky Way CCs and RRLs. In
the present article, we combine the Hipparcos and Gaia DR2 positions to
determine the mean proper motion of the targets, and we search for proper
motion anomalies (PMa) caused by close-in orbiting companions. We identify 57
CC binaries from PMa out of 254 tested stars and 75 additional candidates,
confirming the high binary fraction of these massive stars. For 28 binary CCs,
we determine the companion mass by combining their spectroscopic orbital
parameters and astrometric PMa. We detect 13 RRLs showing a significant PMa out
of 198 tested stars, and 61 additional candidates. We determine that the binary
fraction of CCs is likely above 80%, while that of RRLs is at least 7%. The
newly detected systems will be useful to improve our understanding of their
evolutionary states. The discovery of a significant number of RRLs in binary
systems also resolves the long-standing mystery of their extremely low apparent
binary fraction.
