Hyperpolarization arising from para-hydrogen (p-H-2) can be transferred via carbon-13 to deuterium after hydrogenation of a perdeuterated substrate. The model compound is acetylene-d(2), hydrogenated to yield ethylene-d(2). Transfer to deuterium occurs in ALTADENA experiments (the hydrogenation reaction being performed outside the magnet of the NMR spectrometer prior to the insertion of the sample tube into the NMR probe). The proposed theory, limited to the case where the two p-H-2 protons remain isochronous (same chemical shift), is based on the concept of a steady-state density operator which prevails subsequently to the hydrogenation reaction. The outcome quantity is the carbon-deuterium longitudinal spin order, denoted as (IzIzD)-I-C. Calculations simply involve commutators of all relevant spin quantities with the J-coupling Hamiltonian (denoted as H-J). In particular, it is shown that the necessary condition for polarization transfer toward deuterium via carbon-13 is that (IzIzD)-I-C does not commute with H-J. The structure of H-J is thus of prime importance and it appears that transfer to carbon-13 occurs for both types of experiments, ALTADENA and PASADENA (hydrogenation reaction in the presence of the NMR spectrometer magnetic field). Conversely, transfer toward deuterium via carbon-13 is possible only with ALTADENA experiments. (C) 2003 American Institute of Physics.