A Cinderella plane called the CX will most likely be overshadowed again by the B1 bomber, MX missile and other glamor weapons as the Senate resumes debate next week on how the Pentagon should spend its billions.

But behind the scenes, a fight is raging over who should build the CX cargo plane for carrying war gear to distant places like the Persian Gulf. Opposing lineups include Air Force-Army vs. civilians in the Pentagon; Lockheed vs. McDonnell Douglas in the aerospace industry; Georgia vs. Missouri in Congress.

Rep. Bo Ginn (D-Ga.), who is running for governor of Georgia, has even tried to legislate McDonnell Douglas out of the competition in favor of his home state defense contractor, Lockheed. McDonnell Douglas has threatened to sue the Pentagon if it works out that way.

The battle of the CX, which stands for Cargo Experimental, provides a glimpse of the military-industrial complex in action. Among other things, the CX fight dramatizes how politics, city hall-style, can spill over into the struggle for Pentagon contracts.

On Aug. 28, it sounded like McDonnell Douglas had the CX contract wrapped up. The official Air Force press release said the St. Louis contractor had been selected after seven months of evaluating competing proposals from Boeing and Lockheed. But the Air Force left itself a loophole, declaring "the selection of McDonnell Douglas as the prime contractor does not represent an Air Force commitment to build the CX."

This left open the possibility of settling for a militarized version of the Boeing 747 or Douglas DC10 commercial airliners or an updated Lockheed C5.

In September, Edward C. Aldridge, undersecretary of the Air Force, seemed to have closed that loophole by informing Defense Secretary Caspar W. Weinberger that his service's analyses had concluded that an existing plane would not do the job, that a new plane, the CX, would have to be built. To Air Force professionals, this meant the McDonnell Douglas CX, designated C17, would be its cargo plane of the future.

Neither Lockheed nor Pentagon civilians were willing to accept the C17 as inevitable. Lockheed rushed in with an offer to build 50 C5s at a fixed price.

The Pentagon's research director, Richard D. DeLauer, told The Washington Post that the Lockheed proposal is being evaluated, with the decision expected "in a couple of weeks." An executive of McDonnell Douglas confirmed that his firm had written the Pentagon it would consider an award to Lockheed at this late date a violation of the procurement process and might seek relief in court.

The Army, as well as the Air Force, favors the C17 which would carry Army gear to troublespots. An internal Army memo obtained by The Post states that Pentagon civilians delayed informing Congress about the Air Force rejection of the idea of using existing aircraft.

"Two separate meetings Oct. 13 and 16 have been held with Mr. Frank C. Carlucci deputy secretary of defense and Dr. DeLauer to again present the Army's and the Air Force's position that the C17 is the best airlift aircraft solution for the nation," the memo says.

"During both meetings, Mr. Carlucci acknowledged that the C17 was the aircraft that best met the services' requirements; however, cost was the important factor to sell the program on the Hill. He charged the Air Force to develop comparative data to better determine the cost of the C5 and definitize the Lockheed proposal in order to better compare the two proposals."

Despite this controversy, congressional committees that oversee the Pentagon have shown little interest in delving into the latest CX flap, even though some Air Force leaders are eager to explain why they want the McDonnell Douglas C17, not the Lockheed C5 remake.

The congressional coolness could stem from the disillusionment the committees expressed with previous CX presentations.

Lockheed, possibly to help it counter any adverse Air Force testimony on its C5 proposal, has hired as a consultant former general Alton D. Slay, who was commander of the Air Force Systems Command when he retired in February. It is standard practice among defense contractors to employ retired officers who have access to the old boy network.

Ginn and Sen. Thomas F. Eagleton (D-Mo.) have been busy on behalf of their constituent contractors, Lockheed of Marietta, Ga., and McDonnell Douglas of St. Louis. Ginn, a member of the House Appropriations Committee, managed to get this language in its report on the Pentagon's money bill:

"Considering the present shortfall of airlift capability for the Rapid Deployment Force, the committee has included $50 million for the immediate procurement of the best wide-bodied aircraft for the strategic airlift mission.

"Examples of aircraft in this category include C5s, KC10s, 747s and other wide-bodied aircraft . . . . In view of the position of Congress this year and in previous years, the committee expects the Air Force to proceed immediately with the procurement of wide-bodied cargo aircraft and to abandon the CX program as a substitute."

To McDonnell Douglas, this read like an attempt to overturn Air Force selection of the C17 and pave the way for the Lockheed C5. McDonnell Douglas prevailed upon Eagleton to press the Senate Appropriations Committee to write its Pentagon money bill so as to leave competition open to the C17 as well as existing cargo giants.

This assures a showdown on CX in the House-Senate conference to work out a compromise defense money bill for fiscal 1982.

That is not to say the Senate committee is any more enthusiastic than its House counterpart about spending $12.9 billion to build a new cargo plane. "Significant questions remain" about the best way to meet military airlift requirements, the committee said in denying the Air Force's request for a $169.7 million down-payment on the CX and settling for $15 million for more studies.

The case of the CX indicates that picking tomorrow's weapons is a political process like almost everything else in Washington, the wonders of technology notwithstanding.