||Orbital tuning is central for ice core chronologies beyond annual layer counting, available back to 60 ka (i.e. thousands of years before 1950) for Greenland ice cores. While several complementary orbital tuning tools have recently been developed using delta O-18(atm), delta O-2/N-2 and air content with different orbital targets, quantifying their uncertainties remains a challenge. Indeed, the exact processes linking variations of these parameters, measured in the air trapped in ice, to their orbital targets are not yet fully understood. Here, we provide new series of delta O-2/N-2 and delta O-18(atm) data encompassing Marine Isotopic Stage (MIS) 5 (between 100 and 160 ka) and the oldest part (340-800 ka) of the East Antarctic EPICA Dome C (EDC) ice core. For the first time, the measurements over MIS 5 allow an inter-comparison of delta O-2/N-2 and delta O-18(atm) records from three East Antarctic ice core sites (EDC, Vostok and Dome F). This comparison highlights some site-specific delta O-2/N-2 variations. Such an observation, the evidence of a 100 ka periodicity in the delta O-2/N-2 signal and the difficulty to identify extrema and mid-slopes in delta O-2/N-2 increase the uncertainty associated with the use of delta O-2/N-2 as an orbital tuning tool, now calculated to be 3-4 ka. When combining records of delta O-18(atm) and delta O-2/N-2 from Vostok and EDC, we find a loss of orbital signature for these two parameters during periods of minimum eccentricity (similar to 400 ka, 720-800 ka). Our data set reveals a time-varying offset between delta O-2/N-2 and delta O-18(atm) records over the last 800 ka that we interpret as variations in the lagged response of delta O-18(atm) to precession. The largest offsets are identified during Terminations II, MIS 8 and MIS 16, corresponding to periods of destabilization of the Northern polar ice sheets. We therefore suggest that the occurrence of Heinrich like events influences the response of delta O-18(atm) to precession.