Two of the nation's new strategic nuclear weapons, the air-launched cruise missile and Trident I sub-launched ballistic missile, have now failed operational tests after their deployment, according to Pentagon officials.

Both the Air Force and the Navy have played down the significance of these mishaps, and say the problems associated with the failures either have or will be corrected.

But present and former Pentagon officials, who asked to remain anonymous, yesterday said the failures in operational tests, where the complex weapons systems are operated under simulated combat conditions by regular military personnel rather than trained testing specialists, could become serious over the long term.

Last Dec. 16 the Strategic Air Command announced that the first squadron of B52s armed with cruise missiles had become operational at Griffiss Air Force Base in upstate New York, near Rome.

Three days later, one of those bombers, randomly selected, was armed with an operational missile that had its nuclear warhead removed. The regular SAC ground crew loaded the missile on the plane and the bomber crew flew it to the West Coast. Over the Pacific Ocean, the crew launched its missile along a special test flight route leading toward the Utah test area.

"About 90 minutes into the flight," according to a SAC spokesman, "the missile wandered off course and a chase plane took control of it and flew it down into a landing."

Later, the spokesman said, it was determined that a problem in the computer software of the operational B52 had caused the test to fail.

Eleven days ago, SAC held a second such operational test, again using a randomly selected B52 and cruise missile from Griffiss. This time, according to the spokesman, the missile was launched over the Pacific and flew for three hours "before it departed the control flight path and flew into the ground."

SAC is still studying the test to determine the cause of that accident.

The cruise missile is much like a sophisticated but unmanned aircraft. It flies 500 feet or less above the ground with a forward-looking radar system measuring the distance from the ground and guiding it along a preprogrammed route carried in the missile's on-board computer.

The cruise missile had undergone 20 developmental tests before it was made operational. Five of those tests were partial or complete failures, according to Pentagon sources. But the Air Force felt confident that it could make it operational, according to one official, "because it had 10 straight successes at one point."

An Air Force official added, however, "We let it go operational early because it would serve as a deterrent to the Soviets, even though testing was not completed."

The Trident I sub-launched missile failures first came to public attention when Undersecretary of Defense Richard D. DeLauer told reporters at a breakfast that two of its last five test shots had not worked.

The Navy conducts two types of Trident I tests. One, called demonstration and shakedown operations, involves having a newly armed submarine launch a Trident missile in a controlled test. Of the 16 such tests, three have failed, including one April 19, a Navy spokesman said.

The Navy also holds operational tests where a sub on patrol is recalled to port and one of its missiles has its atomic charge removed. The sub then goes back to sea and at some point is ordered to launch.

The success or failure rate of these tests is classified, but sources said one of the Trident missiles that DeLauer said did not work was part of an operational test.