Let x(t) be a trajectory of the gradient vector field of a C^1 function defined on an open subset of R^n and definable in an o-minimal extension of the real field. We show that this trajectory admits a tangent line at its limit point. The proof is based on the main ideas of [Kurdyka, Mostowski, Parusinski, 2000] and [Kurdyka, Parusinski, 2006], and a geometric analysis of the asymptotic of the spherical part of gradient.