The angle Theta(C(alpha)H(alpha)),NH(N) subtended by the internuclear vectors 13C(alpha)-H(alpha) and 15N-H(N) in doubly-labeled proteins can be determined by observing the effect of cross-correlation between the dipolar interactions on zero- and double-quantum coherences involving 13C(alpha) and 15N. Two complementary 2D experiments with the appearance of 15N-HN correlation spectra yield signal intensities that depend on the rate of interconversion through cross-correlated relaxation of in-phase and doubly antiphase zero- and double-quantum coherences. The ratio of the signal intensities in the two experiments bears a simple relationship to the cross-correlation rate, and hence to the angle Theta(C(alpha)H(alpha),NH(N)). Assuming planarity of the peptide bond, the dihedral angle psi (between C(alpha) and C) can be determined from the knowledge of Theta(C(alpha)H(alpha),NH(N)). The experiments are very time-effective and provide good sensitivity and excellent spectral resolution.