The motion of Earth’s spin axis in space is monitored by Very Long-Baseline Interferometry (VLBI), and since 1994 also its rate is measured by Global Positioning System (GPS). From the direct analysis of the combined VLBI/GPS solution in the interval 1994.3-2004.6 we recently found that the apparent period of the Retrograde Free Core Nutation (RFCN) grew from original 435 days to 460 days during the past ten years, but the resonance effects yielded a stable period of about 430 days. Now we repeat the same study with VLBI-only data, covering much longer interval (1982.4 - 2005.6). Direct analysis shows again a substantial increase of the apparent period during the last decade or so. The resonant period is given by internal structure of the Earth (mainly by the flattening of the core), so it is highly improbable that it is so much variable. From the same observations we derive corrections of certain nutation terms. A subsequent study of indirect determination of resonance RFCN period from the observed forced nutation terms through the resonance effects proves that the natural resonance period remains stable and is equal to 430.32±0.07 solar days. From this follows that an excitation by outer layers of the Earth (atmospheric, oceanic) should exist, with a terrestrial frequency close to that of RFCN (of about -1.0050 cycles per solar day, i.e. with period of -23h53m mean solar time), invoking the apparent changes of the directly observed RFCN period. Thanks to a close proximity of the resonance, any excitation with this period is extremely amplified so that the excitation necessary to explain the difference can be very small. The atmosphere alone contains enough power to excite the observed changes., Jan Vondrák and Cyril Ron., and Obsahuje bibliografii