The investigators propose to conduct a clinical trial to evaluate sertraline treatment efficacy in a large sample of military veterans with a dual diagnosis of PTSD and Alcohol Use Disorder who are receiving Cognitive and Behavioral Therapy as part of the VA-system's new dual diagnosis program. The study is designed as an efficacy trial of sertraline used as an adjunct to Cognitive Behavioral Therapy (CBT) in the treatment of PTSD/Alcohol dual diagnosis. There are two outcomes of interest, namely PTSD symptom improvement and also decreased alcohol consumption. The investigators are interested to know whether or not sertraline is superior to placebo in improving the symptoms of either one or both of these two disorders. Even though sertraline is a treatment of choice for PTSD, the investigators expect that the comorbid condition of alcohol dependence will complicate the treatment of PTSD and that the clustered subgroups will show differential treatment response with sertraline. The primary objective of the present study is to identify subgroups of alcohol dependent persons with PTSD who will either benefit or not benefit from treatment with SSRI's. The proposed study will enroll veterans with PTSD and dually-diagnosed alcohol dependence in a 12-week treatment providing sertraline vs. placebo medication as an adjunct to manualized CBT and will specifically test the hypothesis that subtypes of alcohol dependence can be used to predict which patients respond well and which subgroup responds poorly to SSRI treatment.