Washington — Question: Who has the world's second-largest inventory of combat aircraft? (Hint: It's not a country, but a single service.) Answer: The United States Army, whose 7,000-plus aircraft (mostly helicopters) is outnumbered only by Soviet airpower.
Since the end of World War II, critics have increasingly harped on the overlap in the four armed services' weaponry and their continuous competition over ''roles and missions.''
Why, for example, should the Army, Navy, and Marine Corps all have their own air forces? Why weren't the Air Force and Navy able to agree on a common strategic intercontinental ballistic missile? Why should the Army and Air Force only recently discover that each was asking the same defense contractor to develop a new electronic warfare jammer?
Such fundamental questions point to serious problems that can result in needless expense and perhaps cost lives. In the Grenada invasion, for example, Army airborne and Marine Corps troops had trouble coordinating and communicating vital intelligence data, and this may have prolonged the operation. The failed Iranian hostage-rescue mission involved Marine Corps pilots flying Air Force helicopters from Navy ships to carry Army troops.
It is unlikely that the United States will ever have a single, uniform armed force, as Canada shifted to some years ago. And with the size and complexity of US security interests, few argue that it should. But there are indications that the services are beginning to do better in this regard.
The Army and Air Force this week announced what their service chiefs call ''a historic agreement'' to cut duplicative weapons programs and work together more on battlefield management.
''It's clear that if we go to war, we'll go to war jointly,'' said Gen. John A. Wickham Jr., the Army's chief of staff.
''Roles and missions are not the most important thing,'' added Gen. Charles A. Gabriel, the Air Force chief of staff. ''Doing the job is.''
The fact that the ''memorandum of agreement'' was termed ''historic'' acknowledges the longstanding nature of the problem and indicates that traditional turf-protection and lack of trust will not be easily overcome.
The agreement is the result of a six-month study by both services. It includes 31 points covering composition of annual budgets, duplicative weapons systems, and better coordination on the increasingly complex and fast-paced ''electronic battlefield'' expected in any future war (especially if it were to be waged in Central Europe).
For example, the Army defends against air attack with the Patriot missile and the Air Force does the same thing with its fighters. ''Perhaps it makes sense to have one service manage both of those programs,'' said General Wickham. The Army in turn will play a greater part in defending airbases.
The new announcement follows a pattern that has developed recently. The Air Force and Navy in 1982 strengthened an agreement to have Air Force bombers help protect sea lanes. B-52s now can carry Harpoon antiship missiles. The Defense Department last summer chartered a Munitions Council to coordinate procurement programs.
''Agreement on operating and technical requirements for major systems does not come easily,'' acknowledged Undersecretary of Defense Richard D. DeLauer in congressional testimony last week. He cited earlier failed joint-development efforts (like the JVX tilt-wing aircraft, a hybrid of airplane and helicopter) and urged Congress to press for more service cooperation.
''Vastly greater threats now demand cooperation and efforts to achieve combined effectiveness in ways which could not have been forseen when Congress enacted the Department of Defense charter into law,'' Mr. DeLauer said. ''At the same time, technology and advances in management now offer opportunities that previously appeared beyond our grasp.''
At the same time, DeLauer added, there are cases in which there should be different systems performing the same military mission. ''Common systems have common vulnerabilities,'' he said. ''We must not let capabilities become standardized to the point where they can be neutralized by a single type countermeasure.''
As with reforms to defense weapons procurement, it will take more than pressure from Pentagon civilians to bring about improvements in service cooperation.
It may be that a separate defense procurement agency - independent of the service branches - will have to be created, as Sen. William V. Roth Jr. (R) of Delaware has suggested. A recent study by a CIA analyst concludes that weapons procurement outside the uniformed services (as is the case in most European countries) is much more efficient.
In the United States, military careers can hinge on managing weapons procurement programs. Critics say such uniformed managers are rotated too frequently and have little incentive to defer to other services as sometimes ought to be done. A ''civilian procurement corps,'' says Senator Roth, who chairs the Senate Government Affairs Committee, could alleviate these problems.
The current interest in service cooperation also relates to the continuing debate over the Joint Chiefs of Staff. In recent years, there have been a number of proposals to restructure the JCS so that interservice cooperation is enhanced. The joint staff should be strengthened, many analysts have suggested, and ''rewards'' for spending a part of one's career working with other services should be built in to the military structure.
''Joint agreements among the services are never going to get rid of the problem of interservice rivalries which are really devastating to efficiency,'' says a retired Air Force colonel. ''Without a change in the structure, they're probably doomed to be, if not a complete failure, only a token success.''