Among other longer-than-22-year periods in Fourierspectra of various solar--terrestrial records, the 88-year cycle is unique,because it can be directly linked to the cyclic activity of sunspot formation.Variations of amplitude as well as of period of the Schwabe 11-year cycleof sunspot activity have actually been known for a long time and a ca. 80-yearcycle was detected in those variations. Manifestations of such secular periodicprocesses were reported in a broad variety of solar, solar--terrestrial,and terrestrial climatic phenomena. Confirmation of the existence of the Gleissbergcycle in long solar--terrestrial records as well as the question of itsstability is of great significance for solar dynamo theories. For that perspective,we examined the longest detailed cosmogenic isotope record-INTCAL98calibration record of atmospheric 14C abundance. The mostdetailed precisely dated part of the record extends back to ~11,854 yearsB.P. During this whole period, the Gleissberg cycle in 14Cconcentration has a period of 87.8 years and an average amplitude of ~1?(in Δ14C units). Spectral analysis indicates in frequencydomain by sidebands of the combination tones at periods of ≈91.5 ¿0.1 and ≈84.6 ¿ 0.1 years that the amplitude of the Gleissberg cycleappears to be modulated by other long-term quasiperiodic process of timescale~2000 years. This is confirmed directly in time domain by bandpass filteringand time--frequency analysis of the record. Also, there is additionalevidence in the frequency domain for the modulation of the Gleissberg cycleby other millennial scale processes. Attempts have been made to explain 20thcentury global warming exclusively by the component of irradiance variationassociated with the Gleissberg cycle. These attempts fail, because they requireunacceptably great solar forcing and are incompatible with the paleoclimaticrecords.