The giant pandas of the National Zoo, fresh from a historic first mating on Friday, lapsed into an unfortunately familiar pattern of resentful squabbling yesterday, and by sundown Ling-Ling, the female, had taken a mail-order lover.

Zoo officials said artificial insemination, if not exactly necessary to save the relationship, at least increased prospects for the nation's first native-born baby panda.

It does, however, raise the unsettling possibility that the real father of any such offspring may never be known.

"Frankly, we don't really care about that," said Dr. Devra Kleiman, the zoo's reproductive zoologist. "We may be able to determine that if and when we draw blood from any cub, but we can't be sure."

Ling-Ling's co-respondent in yesterday's affair was the London Zoo's celebrated panda Chia-Chia, whose presence has been a factor in Ling-Ling's life before. Two years ago he flew in for a brief spring stay, but nothing ever came of it.

Yesterday his sperm arrived hand-carried in a chilled test tube via British Airlines jet. This was introduced to an anaesthetized Ling-Ling shortly after 6 p.m. while her hapless mate Hsing-Hsing sulked morosely out of sight next door.

Only Friday Hsing-Hsing had been hailed as a new bear after finally consummating his union with Ling-Ling after seven years of ineffectual attempts. Kleiman and other zoo officials had hoped he could repeat his triumph yesterday, morning, but results were less than satisfactory.

While Hsing-Hsing "had some good mounts," according to Kleiman, they degenerated into the sort of angry backbiting experienced by many sexually frustrated couples.

Ling-Ling, for her part, was "sending out very mixed signals," Kleiman said, angrily summoning her obviously cowed and reluctant partner and then driving him away when he failed to assert himself or rolling over at inopportune moments.

While officials had considered insemination before the coupling took place on Friday, Kleiman said she and other zoo officials decided to go ahead and administer the dose from Chia-Chia rather than obtain a similar dose from Hsing-Hsing.

The London male, is not only younger and stronger than Washington's, his contribution to the reproductive process, zoo officials say, is both greater in volume and more active than that of the hapless Hsing-Hsing, and has, moreover, been proven on the open market. Despite his sexual shutout here two years ago, Chia-Chia fathered a Spanish panda by proxy only last year.

Hsing-Hsing will have one more chance to cement the relationship today, which Kleiman believes will be the last of Ling-Ling's once-a-year fertile period. Ling-Ling, she says, already appears to be going out of heat--a sign that Hsing-Hsing may have done all that was necessary on Friday. No one will really know for three or four months.