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 NMR (NMR). Dipole-dipole (DD) interactions between four nuclei and chem. shift anisotropy (CSA) of two of these nuclei are considered. Two complementary expts. have been designed for 15N,13C-labeled proteins to quantify the effects of cross-correlation between the 13Ca-1Ha and 15N-1HN dipolar interactions on two-spin coherences involving 13Ca of the ith residue with the 15N of the (i+1) the amino acid. Two other expts. allow one to quantify the effect of cross-correlation between the 13C' (carbonyl) CSA and the 13Ca-1Ha dipolar coupling on the relaxation of two-spin coherences involving the 13C' and 13Ca nuclei on the same residue of the protein. These expts. have been used to ext. relevant cross-correlation rates in 15N,13C-labeled human ubiquitin. These rates show a high degree of correlation with the backbone Y angles in proteins. [on SciFinder (R)]