As the Republican presidential nomination seemingly narrows to two candidates, others in the GOP are reportedly seeking a stealth candidate with a military background.

Called the "Warrior Monk" for his dedication to studying war and his refusal to marry or have children, retired U.S. Marine General James Mattis is supposedly being courted by GOP consultants and donors as an alternative to Donald Trump and Ted Cruz.

There is a history of political parties nominating or seeking high-ranking service personnel to run on their tickets. Some military leaders have been lauded, such as George Washington, while others are ridiculed for their ineffectiveness, such as Ulysses Grant.

The following are five military generals who ran or were sought by major parties to run for president:

1. William Henry Harrison

Best remembered today as the president with the shortest tenure, Harrison was regarded as a military hero in the early 19th Century. The Whig Party built his campaign around Harrison's 1811 battle with the slogan, "Tippecanoe and Tyler Too." Harrison delivered the longest inaugural address in history, but by acquiring the nickname "General Mum" from his opponents, there remains doubt about his actual political convictions.

2. Zachary Taylor

Also remembered for serving only a short time before dying in office, Taylor never voted prior to ascending to the presidency. Taylor's achievements came in the Mexican War, where he was known as "Old Rough and Ready." He became a symbol of the war's success and his election in 1848 occurred only months after the Treaty of Guadalupe Hidalgo ended the hostilities.

3. Douglas MacArthur

While still occupying Japan following World War II, MacArthur's name circulated as a possible Republican presidential candidate in 1948. A poor showing in the Wisconsin primary, where the MacArthur family originated, essentially ended any hopes of a political career. In 1952, following his removal as commander in Korea, MacArthur endorsed Sen. Robert Taft for the GOP nomination and delivered the keynote address at the GOP convention.

4. Dwight Eisenhower

Like MacArthur, Eisenhower sought to parlay World War II military honors into a presidential nomination. Unlike MacArthur, Eisenhower was more diplomatic and coyer about his political views. Both parties sought the D-Day commander for the 1948 contest to no avail. According to the memoirs of veteran Washington journalist Arthur Krock, Eisenhower was troubled by Robert Taft's foreign policy views. For that reason, he entered the Republican race where he outmaneuvered Taft for the nomination and ultimately won two decisive electoral victories over Democrat Adlai Stevenson.

5. David Petraeus

Petraeus, commanding general in Iraq and later Afghanistan, was a popular choice for a Republican presidential candidate through 2012. The general's extramarital affair and resignation as director of the CIA scuttled those talks, but his praise of Hillary Clinton in 2014 renewed speculation that he was at least eyeing the VP slot.