On September 23, the high-level General Debate begins, the key event where world leaders deliver speeches before the UNGA. Where is the UNGA held? The Conference Building – This houses the Security Council (UNSC), Trusteeship Council, and Economic and Social Council. – This houses the Security Council (UNSC), Trusteeship Council, and Economic and Social Council. In the UNGA, the rule is: one country, one vote for the delegations that come from every member state.