  We introduce a notion of subunit vector field for fully nonlinear degenerate
elliptic equations. We prove that an interior maximum of a viscosity
subsolution of such an equation propagates along the trajectories of subunit
vector fields. This implies strong maximum and minimum principles when the
operator has a family of subunit vector fields satisfying the H\"ormander
condition. In particular these results hold for a large class of nonlinear
subelliptic PDEs in Carnot groups. We prove also a strong comparison principle
for degenerate elliptic equations that can be written in
Hamilton-Jacobi-Bellman form, such as those involving the Pucci's extremal
operators over H\"ormander vector fields.
