  We study homogeneous geodesics of sub-Riemannian manifolds, i.e., normal
geodesics that are orbits of one-parametric subgroups of isometries. We obtain
a criterion for a geodesic to be homogeneous in terms of its initial momentum.
We prove that any weakly commutative sub-Riemannian homogeneous space is
geodesic orbit, that means all geodesics are homogeneous. We discuss some
examples of geodesic orbit sub-Riemannian manifolds. In particular, we show
that geodesic orbit Carnot groups are only groups of step $1$ and $2$. Finally,
we get a broad condition for existence of at least one homogeneous geodesic.
