We propose to use naltexone to reduce craving for alcohol and cannabis in alcohol and cannabis-dependent patients. We also propose to use established techniques of priming and cue-exposure for alcoholic drinks and cannabis together with measures of [18F] Fluorodeoxyglucose (FDG) in Positron Emission Tomography (PET) imaging in 24 alcohol and cannabis-dependent patients before and after 35 day treatment with naltrexone. We predict that in those who will be successful in quitting alcohol drinking and using cannabis there would be a reduction in alcohol and cannabis cue-induced brain activity in the meso-limbic reward circuit that is responsible for craving for alcohol and cannabis.