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In the United States, if the President dies, resigns, or is somehow removed from office, there is an established line of succession 18 levels deep. These 18 people are never allowed to be too close together, and in case of a big event (ex: State of the Union Address) at least one must not attend.

Also, if the would-be successor does not meet the constitutional requirements for President then the presidency would skip them and go to the next person in the list.

1) Vice President

2) Speaker of the House of Representatives

3) President Pro Tempore of the Senate

4) Secretary of State

5) Secretary of the Treasury

6) Secretary of Defense

7) Attorney General (aka: Secretary of Justice)

8) Secretary of the Interior

9) Secretary of Agriculture

10) Secretary of Commerce

11) Secretary of Labor

12) Secretary of Health and Human Services

13) Secretary of Housing and Urban Development

14) Secretary of Transportation

15) Secretary of Energy

16) Secretary of Education

17) Secretary of Veteran Affairs (thanks CentrX and narzos)

18) Secretary of Homeland Security