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An executive officer is generally a person responsible for running an organization, although the exact nature of the role varies depending on the organization.
While there is no clear line between executive or principal and inferior officers, principal officers are high-level officials in the executive branch of U.S. government such as department heads of independent agencies. In Humphrey's Executor v. United States, 295 U.S. 602 (1935), the Court distinguished between executive officers and quasi-legislative or quasi-judicial officers by stating that the former serve at the pleasure of the president and may be removed at his discretion. The latter may be removed only with procedures consistent with statutory conditions enacted by Congress. The decision by the Court was that the Federal Trade Commission was a quasi-legislative body because of other powers it had, and therefore the president could not fire an FTC member for political reasons. Congress can’t retain removal power over officials with executive function (Bowsher v. Synar). However, statutes can restrict removal if not purely executive (Humphrey’s executor), but can't restrict removal of purely executive officer (Myers v. United States, 272 U.S. 52 (1926)). The standard is whether restriction "impedes the president’s ability to perform his constitutional duty" (Morrison v. Olson, 487 U.S. 654 (1988)).
Corporate law and other legal associations
In business, the executive officers are the top officers of a corporation, the chief executive officer (CEO) being the best-known type. The definition varies; for instance, the California Corporate Disclosure Act defines "executive officers" as the five most highly-compensated officers not also sitting on the board of directors. In many insurance policies, executive officer means, in the case of a corporation, any chairman, chief executive officer, chief financial officer, chief operating officer, president, or general counsel. In the case of a sole proprietorship, an executive officer is the sole proprietor. In the case of a partnership, an executive officer is a managing partner, senior partner, or administrative partner. In the case of a limited liability company, an executive officer is any member, manager, or officer.
In the airline industry, the executive officer, more commonly known as the first officer, is the second in command of the aircraft. In a fixed wing aircraft the first officer sits in the right-hand seat but a rotary wing aircraft they sit on the left.
The term is not used in the British Army or Royal Marines (RM), in which the designation second-in-command (2i/c) is used as a formal appointment. In the Royal Air Force (RAF), the term is informally used between officers and airmen, referring to the officer who is second-in-command. It is formally used in the Royal Navy (RN), however. In smaller vessels, such as submarines and frigates, the executive officer also holds the position of first lieutenant. Originally, the second-in-command was usually referred to as first lieutenant (or as "number one"), although it is becoming more common to hear the term XO. On larger ships, on which the XO holds the rank of commander, the XO is usually referred to simply as "the commander". The XO heads the executive department.
In the United States Army and Marine Corps, for example, there are XO billets in each company, battalion, and brigade, though generally not at higher levels of command until the army level of command. The XO billet is not a command; rather it is considered staff. The XO is typically responsible for the management of day-to-day activities, such as maintenance and logistics, freeing the unit commander to concentrate on tactical planning and execution. The XO also takes charge in the absence of the Commanding Officer. While the experience gained as an XO is highly beneficial for an officer's professional development, it is not necessarily a prerequisite for a command position. At the army level of command, a General will have a Deputy Commander as second in command and an 'Executive Officer' on his personal staff who works as his liaison to the general staff and an aide-de-camp who takes care of his calendar and personal needs.
In the United States Navy and Coast Guard, XOs are normally assigned to all ships and shore units, and have a similar role to their counterparts in the Army and Marine Corps. On board Coast Guard cutters that are commanded by either a junior officer or a senior enlisted member, executive petty officers (XPOs) are usually assigned to serve as second-in-command. On U.S. aircraft carriers, the captain assigned to the ship is an aviator, while the XO is a non-aviator. Amphibious assault ships have the opposite arrangement.
The United States Air Force (USAF) uses the titles of "vice commander" (CV), or "deputy commander" (DC) for an officer who serves as the second-in-command for an organization above squadron level. For a squadron, the second-in-command is typically termed the "director of operations" or "operations officer" (DO). The term "executive officer" is used to designate an officer who serves as an administrative assistant to a senior officer.  In the other uniformed services, this position is usually called an "executive assistant" or "aide-de-camp." The rank of an executive officer can vary from lieutenant (working for a colonel) to a colonel (serving as the executive officer to the Chief of Staff of the Air Force.) 
A unique application of the term is executive officer to the Supreme Allied Commander Europe, and commander, United States European Command. This position is typically held by a brigadier general or rear admiral (LH) and is drawn from all of the armed services. The duties involve serving as both an "executive assistant" to Supreme Allied Commander Europe (SACEUR) and also includes command responsibilities for the U.S. military community at Supreme Headquarters Allied Powers Europe (SHAPE) in Belgium. 
- Air Force Organization, AFI 32-101 http://www.e-publishing.af.mil/shared/media/epubs/AFI38-101.pdf
- The Executive Officer Guide http://www.afmentor.com/mentor/execguide-appendix-b.html Accessed 2012-05-02.
- Biography of Brigadier General Gregory Lengyel, Executive Officer to SACUER (2010-2012) http://archive.is/20120717150747/http://www.af.mil/information/bios/bio.asp?bioID=13949 Accessed on 2012-05-02.