Coherent polarization transfer effects in a coupled spin network have been studied over a wide field range. The transfer mechanism is based on exciting zero-quantum coherences between the nuclear spin states by means of non-adiabatic field jump from high to low magnetic field. Subsequent evolution of these coherences enables conversion of spin order in the system, which is monitored after field jump back to high field. Such processes are most efficient when the spin system passes through an avoided level crossing during the field variation. The polarization transfer effects have been demonstrated for N-acetyl histidine, which has five scalar coupled protons; the initial spin order has been prepared by applying RF-pulses at high magnetic field. The observed oscillatory transfer kinetics is taken as a clear indication of a coherent mechanism; level crossing effects have also been demonstrated. The experimental data are in very good agreement with the theoretical model of coherent polarization transfer. The method suggested is also valid for other types of initial polarization in the spin system, most notably, for spin hyperpolarization.