Is ACT based on behavior analysis?

In a word: yes. Long ago, behavior analysis was relied on by behavior therapists to provide a model of case conceptualization and intervention (e.g., Kanfer & Grimm, 1977; Kanfer & Saslow, 1969) but that idea fell away when clinicians came to believe that behavior analysis could not deal with the issue of cognition. ACT folks were behavior analysts but they agreed that behavior analysis needed to be developed before it could work in this area. ACT, RFT, functional contextualism, and a contextual behavioral science approach was the result of years of work to change that picture. It emerged from behavior analysis, but carries that tradition forward into the experimental analysis of cognitive processes, which extends the armamentarium of behavioral principles and alters many of the key concepts in traditional behavior analysis (e.g., see Barnes-Holmes, Hayes, & Roche, 2003). What has been created in the ACT/RFT/CBS tradition is a different stream of thought within behavior analysis and a different stream of thought within the CBT family of approaches. But it retains all of traditional behavior analysis as well. We are proud to see that as ACT/RFT/CBS has impacted clinical areas it is rekindling an interest in behavior analysis. That in itself is progressive we believe. In the modern era few clinical students are even exposed to a well-crafted course in behavioral principles, taught by a basic scientist knowledgeable in that tradition, which is a sad state of affairs given how robust these principles are. They are even more so when augmented with RFT, greater philosophical clarity, and a renewed development strategy (which is what contextual behavioral science refers to).