A general theoretical approach to coherent transfer of hyperpolarization (HP) among coupled spins is suggested and applied to field-cycling experiments where the polarized spin system is prepared at low magnetic field while observation is performed at high field. The formalism works for an arbitrary mechanism of HP formation and takes into account finite periods of HP preparation, free evolution at the polarization field, and field variation, which was considered in the two limiting regimes of sudden and adiabatic field jump. The polarization transfer is of a coherent nature and proceeds due to strong coupling of spins at low field, where the difference of their Zeeman interaction with the field is less than or comparable to their scalar spin-spin coupling. The case of three nonequivalent coupled spins is studied in detail including the calculation of HP transfer efficiency in the range from zero to high field. Characteristic transfer times are found. New features in the field dependence of polarization are predicted that are due to avoided crossings of the nuclear spin eigenstates of the molecule. The feasibility of HP transfer via spacer spins among spins that have no direct coupling is explored. Another application is the description of para-hydrogen induced polarization in a three-spin system over a wide field range.