The rotational effects of the CH3 and CF3 groups on the electronic structure and nuclear hyperfine coupling constants (HFCCs) in dimethylnitroxide (DMNO center dot) and ditrifluoro-methynitroxide (TFMNO center dot) are investigated using the UB1LYP hybrid density functional method. The CH3 and CF3 HFCCs of both radicals are found to obey the McConnell relation during rotation. The two CH3 groups of the DMNO center dot do not gear with each other, but the rotation of the first CH3 group induces only a small rocking effect (similar to 7 degrees) in the second group. However, in TFMNO center dot, the fluorine atoms from different CF3 groups are close enough so that the steric repulsion between them causes them to act as two interlocked gears, where one drives the other. Therefore, both CF3 groups undergo full rotation. To the best of our knowledge, this is only the second example of "gearing" to be studied. Stabilization due to hyperconjugation is also a major factor that affects the magnitudes of the HFCCs of the CF3 groups during rotational averaging. Stable configurations at specific CF3 group orientations have a large overlap with the NO pi-electron cloud because the lobes of the hybridized p(sigma)(F-2), p(sigma)(F-3), p(sigma)(F-5), and p(sigma)(F-6) orbitals along the F-C bonds have cylindrical symmetry and are of the correct phases for hyperconjugation to occur. The calculated TFMNO center dot C-1-N and C-2-N bond orders range from 0.91 to 0.95 as the CF3 groups are rotated. Therefore, the C-N bonds are essentially single bonds. This, in conjunction with the low rotational energy barrier of approximately 50 cm(-1), explains why the EPR intensities of the F-19 hyperfine splittings, in the range of 163-297 K, are characteristic of six equivalent rapidly rotating fluorine atoms. The TFMNO center dot out-of-plane NO vibrations induce additional s character at the N-14 nucleus. This increases the magnitude of the N-14 HFCC and decreases the F-19 HFCCs. As the temperature increases and because of mixing of the first excited out-of-plane vibrational state, the NO vibrational amplitudes also increase. This leads to an increased N-14 HFCC and decreased F-19 HFCCs, which is in agreement with experiment.