Orbiting companions influence the space motion of their parent star through their gravitational field. Using the Hipparcos and Gaia DR2 (GDR2) catalogues, we determined the long-term proper motion (PM) of the stars common to these two catalogues. We then searched for a proper motion anomaly (PMa) between the long-term PM vector and the GDR2 (or Hipparcos) measurements, indicative of the presence of a perturbing secondary object. We focused our analysis on classical Cepheids, RR Lyrae stars and the nearby stars located within 50 pc. The PMa allows us to detect orbiting companions, down to planetary mass, or set stringent limits on their presence. Approximately 30% of the tested stars within 50 pc present a PMa signal greater than 3σ. We also estimate that > 80% of the Cepheids and ≈ 20% of the RR Lyrae stars are members of binary systems. To complement our PMa-based survey, we also searched the GDR2 for common proper motion companions. We used a simple progressive selection algorithm to separate the most probable candidate companions from the unrelated field stars. This revealed a significant number of candidate gravitationally bound systems with wide separations. We identified 27 Cepheids and 7 RR Lyrae stars in spatially resolved binary systems. The PMa opens the possibility to identify long period orbital companions otherwise inaccessible.