We introduce a model for agent-environment systems where the agents are implemented via feed-forward ReLU neural networks and the environment is non-deterministic. We study the verification problem of such systems against CTL properties. We show that verifying these systems against reachability properties is undecidable. We introduce a bounded fragment of CTL, show its usefulness in identifying shallow bugs in the system, and prove that the verification problem against specifications in bounded CTL is in coNExpTime and PSpace-hard. We present a novel parallel algorithm for MILP-based verification of agent-environment systems, present an implementation, and report the experimental results obtained against a variant of the VerticalCAS use-case.