This study deals with the exploitation of the three classical N-15 relaxation parameters (the longitudinal relaxation rate, R-1, the transverse relaxation rate, R-2, and the H-1-N-15 cross-relaxation rate, sigma (NH)) measured at several magnetic fields in uniformly N-15-labeled proteins. Spectral densities involved in R-1, R-2 and sigma (NH) are analyzed according to the functional form A + B/(1 + omega (2)tau (2)(x)), where tau (s) is the correlation time associated with slow motions sensed by the NH vector at the level of the residue to which it belongs. The coefficient B provides a realistic view of the backbone dynamics, whereas A is associated with fast local motions. According to the "model free approach", B can be identified with 2 tau S-s(2) where S is the generalized order parameter. The correlation time tau (s) is determined from the field dependency of the relaxation parameters while A and B are determined through linear equations. This simple data processing is needed for obtaining realistic error bars based on a statistical approach. This proved to be the key point for validating an extended analysis aiming at the determination of nitrogen chemical shift anisotropy. The protein C12A-p8(MTCP1) has been chosen as a model for this study. It will be shown that all data (obtained at five magnetic field strengths corresponding to proton resonance of 400, 500, 600, 700, and 800 MHz) are very consistently fitted provided that a specific effective correlation time associated with slow motions is defined for each residue. This is assessed by small deviations between experimental and recalculated values, which, in all cases, remain within experimental uncertainty. This strategy makes needless elaborate approaches based on the combination of several slow motions or their possible anisotropy. Within the core of the protein tau (s) fluctuates in a relatively narrow range (with a mean value of 6.15 ns and a root-mean-square deviation of 0.36 ns) while it is considerably reduced at the protein extremities (down to similar to3 ns). To a certain extent, these fluctuations are correlated with the protein structure. A is not obtained with sufficient accuracy to be valuably discussed. Conversely, order parameters derived from B exhibit a significant correlation with the protein structure. Finally, the multi-field analysis of the evolution of longitudinal and transverse relaxation rates has been refined by allowing the N-15 chemical shift anisotropy (csa) to vary residue by residue. Within uncertainties (derived here on a statistical basis) an almost constant value is obtained. This strongly indicates an absence of correlation between the experimental value of this parameter obtained for a given residue in the protein, the nature of this residue, and the possible involvement of this residue in a structured area of the protein.