  Self-propulsion of a Janus droplet in a solution of surfactant, which reacts
on a half of a drop surface, is studied theoretically. The droplet acts as a
catalytic motor creating a concentration gradient, which generates its
surface-tension-driven motion; the self-propulsion speed is rather high, $60\;
{\rm \mu m/s}$ and more. This catalytic motor has several advantages over other
micromotors: simple manufacturing, easily attained neutral buoyancy. In
contrast to a single-fluid droplet, which demonstrates a self-propulsion as a
result of symmetry breaking instability, for Janus one no stability threshold
exists; hence, the droplet radius can be scaled down to micrometers.
  The paper was finalized and submitted by Denis S. Goldobin after Sergey
Sklyaev had sadly passed away on June 2, 2014.
