HMS Ajax (1767) was a 74-gun third-rate ship of the line of the Royal Navy. Designed by William Bately, she was the name ship of the Ajax-class of ships of the line, which also included HMS Egmont. The vessel was ordered on October 21, 1763, and the keel was laid down at Portsmouth Dockyard in September 1764. The ship was launched on December 23, 1767.
As a 74-gun ship, the Ajax was part of the backbone of the British fleet during the late 18th century, designed to provide a balance between firepower and sailing qualities. The vessel's dimensions included a gundeck length of 166 feet 6 inches and a beam of 47 feet.
HMS Ajax saw significant service during the American Revolutionary War. In January 1780, she was part of Admiral Sir George Rodney's fleet at the Battle of Cape St. Vincent (also known as the Moonlight Battle), where the British fleet defeated a Spanish squadron. In 1781, the ship participated in the Battle of the Chesapeake under Rear-Admiral Thomas Graves, a strategic engagement that led to the eventual British surrender at Yorktown.
In April 1782, HMS Ajax fought in the Battle of the Saintes under Admiral Rodney, an engagement in the Caribbean against a French fleet commanded by the Comte de Grasse. During this battle, the ship served in the center division of the British line.
Following the conclusion of the war, the ship was paid off and returned to England. HMS Ajax was sold for breaking up in February 1785, as she was no longer considered fit for active service.