The effects of delayed feedback terms on nonlinear oscillators are very important. In order to study the effect of delayed terms on system vector fields,firstly,using center manifold reduction and normal form method, we compute and analyze that the system appears Zero-Hopf bifurcation when its characteristic equation has a simple zero root and a pair of purely imaginary roots and all other roots have negative real parts. Then,we clarity that a class of delayed nonlinear oscillators show different bifurcation when the delayed terms change via numerical simulation of specific examples. It’s significant to investigate the other different systems further and what types of bifurcations may occur on systems.