We have developed a universal method to form the reference signal for the stabilization of arbitrary atomic clocks based on Ramsey spectroscopy. Our approach uses an interrogation scheme of the atomic system with two different Ramsey periods and a specially constructed combined error signal (CES) computed by subtracting two error signals with the appropriate calibration factor. CES spectroscopy allows for perfect elimination of probe-induced light shifts and does not suffer from the effects of relaxation, time-dependent pulse fluctuations and phase-jump modulation errors and other imperfections of the interrogation procedure. The method is simpler than recently developed autobalanced Ramsey spectroscopy techniques (Sanner et al 2018 Phys. Rev. Lett. 120 053602; Yudin et al 2018 Phys. Rev. Appl. 9 054034), because it uses a single error signal that feeds back on the clock frequency. The use of CES is a general technique that can be applied to many applications of precision spectroscopy.clocks were theoretically described in [27], which proposed the use of pulses of differing durations ( 1 2 t t ¹ ) and the use of composite pulses instead of the standard Ramsey sequence with two equal π/2 pulses. This 'hyper-Ramsey' scheme has been successfully realised in an ion clock based on an octupole transition in Yb + [5,28], where a suppression of the light shift by four orders of magnitude and an immunity against its fluctuations were demonstrated. Further developments in Ramsey spectroscopy resulted in additional suppression of probe-fieldinduced frequency shifts. For example, the hyper-Ramsey approach uses new phase variants to construct error signals [29][30][31][32] to significantly suppress the probe-field-induced shifts in atomic clocks. However, as was shown in [33], all previous hyper-Ramsey methods [5, 27-29, 31, 34] are sensitive to decoherence and spontaneous relaxation, which can prevent the achievement of state-of-the-art performance in some systems. To overcome the effect of decoherence, a more complicated construction of the error signal was recently proposed in [35], which requires four measurements for each frequency point (instead of two) combined with the use of the generalized hyper-Ramsey sequences presented in [31]. Nevertheless the method in [35] is not free from other disadvantages related to technical issues such as time-dependent pulse area fluctuations and/or phase-jump modulation errors during the measurements.The above approaches [5, 27-29, 31, 34, 35] are all one-loop methods, since they use one feedback loop and one error signal. However, frequency stabilization can also be realized with two feedback loops combined with Ramsey sequences with different dark periods T 1 and T 2 [33,36,37]. For example, the synthetic frequency protocol [33] in combination with the original hyper-Ramsey sequence [27] allows for substantial reduction in the sensitivity to decoherence and imperfections of the interrogation procedure. Auto-balanced Ramsey spectroscopy (ABRS) is another effective approach that was ...