High-resolution magic-angle spinning (MAS) solid-state nuclear magnetic resonance (NMR) spectroscopy exploiting the dipole-dipole coupling between unlike spins is a powerful tool for the study of structure and dynamics. In particular, the rotational-echo double-resonance (REDOR) technique has established itself as a method for probing heteronuclear dipole-dipole couplings in isotopically dilute systems of low-gamma nuclei. In organic substances it is, however, particularly advantageous to consider heteronuclear spin-pairs such as H-1-C-13, on account of the high natural abundance of H-1 and thus a much wider range of possible applications, such as the determination of order parameters in liquid crystals and polymer melts. We describe the possibility of performing C-13-observed REDOR in H-1-C-13 systems, where very-fast MAS with spinning frequencies of up to 30 kHz is used to successfully suppress the perturbing homonuclear couplings among the protons, which would usually be expected to hamper a proper data analysis. Simple modifications of the REDOR experiment are presented which lead to a two-dimensional experiment in which heteronuclear multi-spin multiple-quantum modes are excited, the evolution of which is monitored in the indirect frequency dimension. The existence of higher quantum orders in the proton subspace of these heteronuclear coherences is proven by performing a phase-incremented spin-counting experiment, while a phase cycle can be implemented which allows the observation of specific selected coherence orders in the indirect dimension of two-dimensional shift correlation experiments. The significance of the heteronuclear approach to spin counting is discussed by comparison with well-known homonuclear spin-counting strategies. For the shift correlation, the high resolution of H-1 chemical shifts in the indirect dimension is achieved by the use of high B-0 fields (omega (1H)(L)/2 pi =700.13 MHz) combined with very-fast MAS, and dipolar coupling information can be extracted by analyzing either peak intensities or spinning-sideband patterns in the indirect frequency dimension. The method is termed dipolar heteronuclear multiple-spin correlation (DIP-HMSC). (C) 2001 American Institute of Physics.