A separation technique that divides the transport equation into two parts is developed to analyze fusion-fission hybrid systems. The transport of fusion-produced neutrons (first generation neutrons) is separately calculated and a fission neutron source is generated. The behavior of the second and subsequent generations of neutrons is obtained using fewer energy groups and a low order treatment for scattering. As usual, integral parameters are the summation of the contributions from the two parts. A sensitivity theory consistent with the separation technique is used to evaluate the relative sensitivity coefficient of a reaction rate to perturbations in the system. Relations between different adjoint fluxes are derived in the context of the separation technique. The technique is applied to show that the use of a low-order scattering description when solving the second part of the problem leads to small errors in the value of the fissile fuel production rate in a hybrid. Variation of this production rate with time can approximately be accounted for using the beginning-of-life values of the forward flux of the first part (related to fusion neutrons), the adjoint flux of the system, and the time-dependent source of the second part (related to subsequent fission generations).