  Self-sustained oscillators (SSOs) is a commonly used method to generate
classical clock signals and SSOs using delayed feedback have been developed
commercially which possess ultra-low phase noise and drift. Research into the
development of quantum self-oscillation, where one can also have a periodic and
regular output {\em tick}, that can be used to control quantum and classical
devices has received much interest and quantum SSOs so far studied suffer from
phase diffusion which leads to the smearing out of the quantum oscillator over
the entire limit cycle in phase space seriously degrading the system's ability
to perform as a self-oscillation. In this paper, we explore quantum versions of
time-delayed SSOs, which has the potentials to develop a ticking quantum clock.
We first design a linear quantum SSO which exhibits perfect oscillation without
phase diffusion. We then explore a nonlinear delayed quantum SSO but find it
exhibits dephasing similar to previously studied non-delayed systems.
