  In this paper, we investigate the stability problem of subelliptic harmonic
maps with potential. First, we derive the first and second variation formulas
for subelliptic harmonic maps with potential. As a result, it is proved that a
subelliptic harmonic map with potential is stable if the target manifold has
nonpositive curvature and the Hessian of the potential is nonpositive definite.
We also give Leung type results which involve the instability of subelliptic
harmonic maps with potential when the target manifold is a sphere of dimension
$\geq 3$.
