A comprehensive description is presented of the effects on two-spin coherences (i.e., superpositions of zero- and double-quantum coherences) of cross-correlation between the fluctuations of two different relaxation mechanisms in nuclear magnetic resonance (NMR). Dipole-dipole (DD) interactions between four nuclei and chemical shift anisotropy (CSA) of two of these nuclei are considered. Two complementary experiments have been designed for N-15,C-13-labeled proteins to quantify the effects of cross-correlation between the Ca-13(alpha)-(1)Ha(alpha) and N-15-H-1(N) dipolar interactions on two-spin coherences involving C-13(alpha) of the ith residue with the N-15 Of the (i+1)th amino acid. Two other experiments allow one to quantify the effect of cross-correlation between the C-13' (carbonyl) CSA and the (Calpha-1Halpha)-C-13 dipolar coupling on the relaxation of two-spin coherences involving the C-13' and C-13(alpha) nuclei on the same residue of the protein. These experiments have been used to extract relevant cross-correlation rates in N-15,C-13-labeled human ubiquitin. These rates show a high degree of correlation with the backbone Psi angles in proteins.