The potential of a combined and simultaneous fast-neutron/gamma-ray computed tomography technique using Monte Carlo simulations is described. This technique is applied on the basis of a hypothetical tomography system comprising an isotopic radiation source (americium-beryllium) and a number (13) of organic scintillation detectors for the production and detection of both fast neutrons and gamma rays, respectively. Via a combination of gamma-ray and fast neutron tomography the potential is demonstrated to discern nuclear materials, such as compounds comprising plutonium and uranium, from substances that are used widely for neutron moderation and shielding. This discrimination is achieved on the basis of the difference in the attenuation characteristics of these substances. Discrimination of a variety of nuclear material compounds from shielding/moderating substances (the latter comprising lead or polyethylene for example) is shown to be challenging when using either gamma-ray or neutron tomography in isolation of one another. Much-improved contrast is obtained for a combination of these tomographic modalities. This method has potential applications for in-situ, nondestructive assessments in nuclear security, safeguards, waste management and related requirements in the nuclear industry.