This increasing role of highly automated and intelligent systems as team members has started a paradigm shift from human-human teaming to Human-Autonomy Teaming (HAT). However, moving from human-human teaming to HAT is challenging. Teamwork requires skills that are often missing in robots and synthetic agents. It is possible that adding a synthetic agent as a team member may lead teams to demonstrate different coordination patterns resulting in differences in team cognition and ultimately team effectiveness. The theory of Interactive Team Cognition (ITC) emphasizes the importance of team interaction behaviors over the collection of individual knowledge. In this dissertation, Nonlinear Dynamical Methods (NDMs) were applied to capture characteristics of overall team coordination and communication behaviors. The findings supported the hypothesis that coordination stability is related to team performance in a nonlinear manner with optimal performance associated with moderate stability coupled with flexibility. Thus, we need to build mechanisms in HATs to demonstrate moderately stable and flexible coordination behavior to achieve team-level goals under routine and novel task conditions.