  Homoclinic tangencies and singular hyperbolicity are involved in the Palis
conjecture for vector fields. Typical three dimensional vector fields are well
understood by recent works. We study the dynamics of higher dimensional vector
fields that are away from homoclinic tangencies. More precisely, we prove that
for \emph{any} dimensional vector field that is away from homoclinic
tangencies, all singularities contained in its robustly transitive singular set
are all hyperbolic and have the same index. Moreover, the robustly transitive
set is {$C^1$-generically }partially hyperbolic if the vector field cannot be
accumulated by ones with a homoclinic tangency.
