Abstract: Two new bifurcations in time-delayed power systems,the oscillation disappearance bifurcation（ODB）and oscillation emergence bifurcation（OEB）found in a previous study,are explored and discussed.Their definitions are given first according to the transform of the system eigenvalues.Further,an approach to determining the occurrence of ODB and OEB in timedelayed dynamic systems is proposed.It uses the information on the disappearance and emergence of the real solution branches of the Lambert W function.A typical one-dimensional time-delayed system and WSCC 3-machine-9-bus system with time delay are then selected to show the mechanism of two bifurcations and to validate the given approach.Since OEB and ODB are closely related to the emergence and disappearance of the system oscillation modes,the study under discussion is helpful to power system stability analysis with time delays.