  The next generation of atomic frequency standards based on an ensemble of
neutral atoms or a single-ion will provide very stringent tests in metrology,
applied and fundamental physics requiring a new step in very precise control of
external systematic corrections. In the proceedings of the 8th Symposium on
Frequency Standards and Metrology, we present a generalization of the recent
Hyper-Ramsey spectroscopy with separated oscillating fields using composites
pulses in order to suppress field frequency shifts induced by the interrogation
laser itself. Sequences of laser pulses including specific selection of phases,
frequency detunings and durations are elaborated to generate spectroscopic
signals with a strong reduction of the light-shift perturbation by off resonant
states. New optical clocks based on weakly allowed or completely forbidden
transitions in atoms, ions, molecules and nuclei will benefit from these
generalized Ramsey schemes to reach relative accuracies well below the
10$^{-18}$ level.
