In this study, the adaptive fuzzy collision-free formation control issue is investigated for uncertain nonlinear multiagent systems (MASs) under communication delays. Fuzzy logic systems (FLSs) are applied to model unknown agents, and the navigation function is utilized to establish the criterions of collision avoidance and connectivity preservation for the agents. Since the communication between agents is affected by time-varying delays, the leader's state and its high-order derivatives' real-time information are unknown, a distributed command governor is designed to estimate them. Based on the designed distributed command governor, and the collision avoidance and connectivity preservation criterions, an adaptive fuzzy collision-free formation control approach is formulated by backstepping control design theory. The developed adaptive fuzzy formation control approach can not only achieve the formation objective, but also avoid the collisions and ensure the topology connectivity. Finally, we apply the developed adaptive fuzzy formation control method to multiple Euler-Lagrangian (EL) systems, the simulation and comparison results verify its effectiveness.