This paper considers Hopf bifurcation of ordinary
differential systems along the singular direction in the
parameter plane. Hopf Bifurcation of the same system along non-singular directions
have been studied recently in . As an application of our main results,
we also obtain results of existence and non-existence for a type of degenerate Hopf
bifurcation (i.e., the type without transversality) for one parameter ODE systems.