By analogy to heteronuclear systems, coherence can be transferred adiabatically in the rotating frame between two selected spins I and S belonging to a homonuclear network of scalar-coupled spins. In contrast to cross polarization with const. radiofrequency field amplitudes, the transfer function obtained with adiabatic methods depends in a monotonic, nonoscillatory manner on the duration of the transfer interval. The efficiency of the transfer does not depend on the magnitude of the scalar coupling const. JIS, although it can be affected by relaxation and by couplings JIR and JSR to further spins R. Three methods were studied: (i) adiabatic demagnetization of spin I in the rotating frame followed by observation of the resulting J-ordered state, (ii) adiabatic demagnetization of spin I in the rotating frame followed by adiabatic remagnetization of spin S, and (iii) adiabatic transfer were spins I and S are subjected simultaneously to time-dependent spin-locking fields. In all three cases, the optimum shape of the time dependence of the radiofrequency field amplitudes is discussed, with the help of a geometric interpretation of cross polarization. [on SciFinder (R)]