The computer time saving attainable by solving the transport equation for the higher neutron energy groups and the diffusion equation for the lower energy groups was investigated for fusion reactor safety applications. For the ARIES-I design considered, it was found that coupled diffusion-transport solutions can provide the activation rates in all the zones excluding the shield to within 2.5 % and 5 % when the transition to the diffusion approximation is, respectively, at 1.4 MeV and 8.8 MeV. The corresponding saving in CPU time relative to an all-transport solution is 31 % and 43 %. For the low order transport approximation used, this CPU time is significantly shorter than that required by ONEDANT, with its built-in diffusion synthetic acceleration.