The theory of single-transition cross-polarization in nuclear magnetic resonance is presented and verified by experimental evidence. In comparison to conventional cross-polarization a qualitative change in the mechanism is observed. Under the influence of matched radio-frequency fields with amplitudes that are smaller than the scalar coupling constant J(IS) for a two-spin system with I=1/2 and S=1/2 in isotropic solution, two simultaneous coherence transfer processes are observed between single-transition coherences which have phases that are parallel to those of the radio-frequency fields, an on-resonance transfer from SxIalpha to (SIx)-I-alpha and an off-resonance transfer from SxIbeta to (SIx)-I-beta, without mixing between the two pathways. Coherence transfer is also observed between single-transition coherences with phases that are perpendicular to the radio-frequency fields, from SyIalpha to (SIy)-I-alpha and from SyIbeta to (SIy)-I-beta, as well as between longitudinal components, from SzIalpha to (SIz)-I-alpha and from SzIbeta to (SIz)-I-beta. The transfer may therefore be considered quasi-isotropic. We consider the conditions under which such transfer processes can be observed. Coherence transfer is affected by differential relaxation due to cross-correlation effects.