  The notion of a parallelizable distribution has been introduced and
investigated. A non-integrable parallelizable distribution carries a natural
sub-Riemannian structure. The geometry of this structure has been studied from
the bi-viewpoint of absolute parallelism geometry and sub-Riemannian geometry.
Two remarkable linear connections have been constructed on a sub-Riemannian
parallelizable distribution, namely, the Weitzenb\"ock connection and the
sub-Riemannian connection. The obtained results have been applied to two
concrete examples: the spheres $S^3$ and $S^7$.
