  Circular orbits of spinning test particles and their stability in
Schwarzschild-like backgrounds are investigated. For these space-times the
equations of motion admit solutions representing circular orbits with particles
spins being constant and normal to the plane of orbits. For the de Sitter
background the orbits are always stable with particle velocity and momentum
being co-linear along them. The world-line deviation equations for particles of
the same spin-to-mass ratios are solved and the resulting deviation vectors are
used to study the stability of orbits. It is shown that the orbits are stable
against radial perturbations. The general criterion for stability against
normal perturbations is obtained. Explicit calculations are performed in the
case of the Schwarzschild space-time leading to the conclusion that the orbits
are stable.
