  Given a Carnot-Carath\'eodory metric space $(R^n, d_{\hbox{cc}})$ generated
by vector fields $\{X_i\}_{i=1}^m$ satisfying H\"ormander's condition, we prove
in theorem A that any absolute minimizer $u\in W^{1,\infty}_{\hbox{cc}}(\Om)$
to $F(v,\Om)=\sup_{x\in\Om}f(x,Xv(x))$ is a viscosity solution to the Aronsson
equation (1.6), under suitable conditions on $f$. In particular, any AMLE is a
viscosity solution to the subelliptic $\infty$-Laplacian equation (1.7). If the
Carnot-Carath\'edory space is a Carnot group ${\bf G}$ and $f$ is independent
of $x$-variable, we establish in theorem C the uniquness of viscosity solutions
to the Aronsson equation (1.13) under suitable conditions on $f$. As a
consequence, the uniqueness of both AMLE and viscosity solutions to the
subelliptic $\infty$-Laplacian equation is established in ${\bf G}$
