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 π/4 or 3π/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. PACS numbers: 32.80.Qk,32.70.Jz,06.20.Jr The next generation of optical-frequency standards based on an ensemble of neutral atoms or a single-ion will provide new very stringent tests in metrology, applied and fundamental physics [1]. Atomic clocks using cold fermionic species trapped in 1D optical lattices [2], now surpassing the accuracy of caesium atomic fountains, have clearly demonstrated the potential to establish a breakthrough in ultra-high precision measurement achieving soon a relative 10 −18 level of accuracy. For both bosonic and fermionic species, the cold collisions and the light-shifts contributions from the optical lattice or from the probe laser have been intensively explored and mitigated [3,4]. In a recent investigation of the fermionic 87 Sr optical lattice clock [5], the lattice and the probe laser light-shift corrections were characterized at the 1 × 10 −18 relative level of uncertainty. Instead probe light-shifts represent a non negligeable issue for clocks based on bosonic neutral atoms with forbidden dipole transitions activated by mixing static magnetic field with a single laser [6-9], for clocks with magic-wave induced transition in even isotopes [10], with E1-M1 two-photon laser excitations [11][12][13], for ionic systems with a single particle or highly charged systems [14,15], and molecular clocks [16]. Light-shifts are also important issues in high resolution spectroscopy and tests of theories [17].In order to reduce shifts and broadening due to inhomogeneous excitation conditions or shifts that are the result of the clock laser excitation itself, sequence of composite excitation pulses based on generalization of the Ramsey scheme [18] to more complex ones in- * E-mail address: thomas.zanon@upmc.fr cluding additional intermediate pulses with suitably selected frequency and phase steps have been introduced. These new techniques are denoted as Hyper-Ramsey HR schemes [19] or Generalized Hyper-Ramsey GHR resonances [20], and were recently proposed...