I conducted two studies. First, I examined the applicability of discrete-trial functional analysis (DTFA) for identifying the function of problem behavior in three adults with a dual diagnosis of a significant intellectual disability and a mental illness. Results indicated clear patterns of problem behavior for each participant. Second, I used a multiple-baseline design across participants (Kazdin, 2011) to assess the effectiveness of FCT on the acquisition and discriminated use of a functionally equivalent replacement behavior. Results indicated that FCT was effective in producing acquisition and discriminated use of a replacement response for all participants. This study extends the literature on the accurate assessment of the function of problem behavior to adults with dual diagnosis and provides empirical evidence of the effects of one's motivation on the acquisition of a functionally equivalent replacement behavior. Implications for future research and practice are suggested. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]