Axeman,
When displayed in Joint formation, the order of precedence is Army, MARINES, Navy..then the other guys. After WWII the SecDef directed the above when in joint formations. Many, many, many arguments over this, but check out a picture of a joint formation at the Pentagon - Army, Marines, Navy..then the other guys.
Semper fi,
Jim
EDIT - Wolfhound is correct on the establishment dates, but....I forget the DoD or OSD order that applies, but in my career I've had to look it up a few times...you would think I'd remember it wouldn't you!!
Yet another edit -- here you go:
When different services are in formation, the following order of precedence should be followed:
Cadets, United States Military Academy
Midshipmen, United States Naval Academy
Cadets, United States Air Force Academy
Cadets, United States Coast Guard Academy
Midshipmen, United States Merchant Marine Academy
United States Army
United States Marine Corps
United States Navy
United States Air Force
United States Coast Guard
Army National Guard of the United States
Army Reserve
Marine Corps Reserve
Naval Reserve
Air National Guard of the United States
Air Force Reserve
Coast Guard Reserve
Other training organizations of the Army, Marine Corps, Navy, Air Force, and Coast Guard, in that order
Big formation!!