We present a general theory of coherent isotropic averaging in nuclear magnetic resonance (NMR). In a zero external field, magnetic-field pulses can selectively average the internal spin Hamiltonians, while preserving the intrinsic invariance of the spectrum with respect to the sample orientation. The theory predicts the limits of the scaling factors for tenser interactions of different ranks. Time reversal is found to be possible for first- and second-rank tensors with scaling factors of -1/3 and -1/4, respectively. Explicit sequences, based on icosahedral symmetry, are given for a number of optimal scaling factors. To illustrate the theory, an experiment is also presented in the special case of rank-selective decoupling. As in high-field NMR, applications can be expected from the introduction of coherent averaging schemes for zero-held techniques : for example, decouplings (by rank or nuclear species), time reversal, and multipolar experiments (zero-field analog of multiple-quantum NMR).