  We present a new interrogation scheme for the next generation of quantum
clocks to suppress frequency-shifts induced by laser probing fields themselves
based on Generalized Hyper-Ramsey resonances. Sequences of composite laser
pulses with specific selection of phases, frequency detunings and durations are
combined to generate a very efficient and robust frequency locking signal with
almost a perfect elimination of the light-shift from off resonant states and to
decouple the unperturbed frequency measurement from the laser's intensity. The
frequency lock point generated from synthesized error signals using either
$\pi/4$ or $3\pi/4$ laser phase-steps during the intermediate pulse is tightly
protected against large laser pulse area variations and errors in potentially
applied frequency shift compensations. Quantum clocks based on weakly allowed
or completely forbidden optical transitions in atoms, ions, molecules and
nuclei will benefit from these hyper-stable laser frequency stabilization
schemes to reach relative accuracies below the 10$^{-18}$ level.
