  We show that the necessary and sufficient condition for erecting locally
inertial coordinates at a point $p$ of a $U^4$-space, and therefore assuring
the validity of the equivalence principle at that point, is the vanishing at
$p$ of the symmetric part of the contortion tensor. This fact does not demand a
vanishing torsion, but only a totally antisymmetric one. As an application, we
derive the geodesic deviation equation; and prove the compatibility with the
Newtonian limit.
