Relational systems—including interpersonal relationships, organizations, political institutions, and civilizations—exhibit patterns of emergence, stability, and collapse that remain insufficiently explained by existing resource-based, institutional, or behavioral theories alone. This paper introduces Relational Regime Theory, a system dynamics framework proposing that the trajectory of relational systems is determined by the dominant feedback loop structure governing agent interactions. Specifically, relational systems stabilize within one of three fundamental regimes, corresponding to distinct game-theoretic payoff structures. In the cooperative regime (positive-sum game), mutually reinforcing feedback loops increase the capacity and stability of participating agents, generating cumulative growth and systemic resilience. In the competitive regime (zero-sum game), balancing feedback loops regulate relative advantage without increasing total system capacity, resulting in dynamic equilibrium. In the destructive regime (negative-sum game), mutually reinforcing destructive feedback loops reduce the capacity of participating agents, initiating self-reinforcing dynamics of systemic degradation and collapse, wherein all agents incur net losses. The paper further formalizes regime transitions and demonstrates that sustainability corresponds to the persistence of cooperative (positive-sum) dynamics with competition constrained below thresholds that trigger destructive (negative-sum) feedback loops. This framework is scale-independent and applies uniformly across interpersonal, organizational, and civilizational domains. By identifying relational regimes and their associated sum structures as the primary endogenous determinants of system trajectory, Relational Regime Theory provides a unified structural account of emergence, sustainability, and collapse in relational systems.