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We propose a model of the internal organization of legislatures in presidential, semi-presidential, and parliamentary political systems. As in Diermeier, Prato and Vlaicu (2015) legislators choose policy from a unidimensional policy in a proposer-pivot model. Legislators are risk-averse. Proposers are randomly chosen with probabilities determined by an endogenous organizational structure previously determined by the legislature. We consider various types of presidential systems with presidential veto rights and override thresholds. The case of no veto rights corresponds to a parliamentary system. We also consider the case where an exogenously determined executive has proposal rights, as common in semi-presidential systems and constitutional monarchies. We fully analyze the equilibria for all cases and compare their implications. In a parliamentary system a legislature has an incentive to centralize proposal power to reduce the uncertainty associated with a decentralized legislature. Having veto right with a high override threshold reduces the incentives for delegation. The allocation of proposal rights, however, is non-monotonic, and legislatures delegate more procedural power to legislators oppose to presidents with stronger proposal rights or more extreme policy positions. We also consider systems where the president determines the organizational structure, e.g. by appointing a prime minister, as in France, veto power at the procedural stage, presidents with proposal power at the policy stage, as well as presidents with outside options, e.g., the use of referenda. The model provides a rich comparative framework to study the effects of constitutional structures on legislative organizations and policy making.