Peking — ''Welcome, welcome, warmly welcome!'' sang the schoolgirls as they danced with bouquets and tambourines. Across the vast Tian An Men Square floated the rarely heard strains of ''God Save the Queen.''
The occasion: Margaret Thatcher's visit to China, the first by a British prime minister in office. She is receiving red-carpet treatment in Peking, featuring talks with all three of China's top leaders - Deng Xiaoping, Hu Yaobang, and Zhao Ziyang.
But a potential problem looms over the proceedings. The success of Mrs. Thatcher's visit depends on how well she and her hosts can sidestep the delicate question of sovereignty over Hong Kong.
If it were not for the Hong Kong issue, there would be nothing particularly sensitive about Mrs. Thatcher's visit. It repays then-Premier Hua Guofeng's visit to Britain three years ago. Mr. Hua has since lost all his party and government posts except membership on the Central Committee.
Mrs. Thatcher will discuss global strategic issues, where Peking agrees with her tough anti-Soviet stance but supports Argentine sovereignty over the Falklands. She will undoubtedly promote British exports, especially of defense items, for which the Chinese have window-shopped assiduously without so far writing out any checks.
But Hong Kong will be the key issue, one that requires the ''Iron Lady'' to show great tact. Britain and China are engaged in a mutual search for a formula that will safeguard Hong Kong's capitalistic prosperity while acknowledging, or appearing to acknowledge, Chinese sovereignty over what is now a British crown colony.
Talks so far have been informal and indirect, but Mrs. Thatcher's visit is expected to kick off a more formal negotiating process.
Hong Kong's status is complicated. Hong Kong Island and a tiny strip of the mainland were ceded to Britain in perpetuity in two agreements in the mid-1800s. The other 365 square miles - 90 percent of the colony - were leased to Britain for 99 years in l898.
Without the leased territory Hong Kong is not viable, and the colony's ordinary citizens as well as rich investors want to know well in advance of the lease's expiration what Peking intends to do.
China's attitude is twofold.
First, China's sovereignty over all Hong Kong must be acknowledged. Second, Hong Kong's economic prosperity must be safeguarded. China, after all, earns 40 percent of its foreign exchange from the colony.
One solution is a Peking guarantee that, after acknowledging Chinese sovereignty, Hong Kong would continue to enjoy a special status within the communist orbit. Peking, it seems, would prefer this solution - if it was sufficient to reassure Hong Kong's citizens.
But Hong Kong observers maintain that the colony's prosperity as a center of free enterprise depends as much on the framework of British law and administration as it does on the hard work of its overwhelmingly Chinese population or of the millions of dollars brought in by outside investors.
Some Hong Kong citizens have suggested Chinese sovereignty and continued British rule under some sort of management contract as a possible solution. Mrs. Thatcher is said to have brought ''some ideas'' with her that she will put to the Chinese leadership. What specific ideas may be included has not as yet been divulged.
The whole question is too complicated to be solved by a single prime ministerial visit. But language sufficient at least to partially allay the anxieties of 5 million British-ruled Chinese in Hong Kong will have to emerge.
Most of these Chinese, without actually saying so, would prefer British rule to continue. But they are not at all like the Falklanders, for they acknowledge that they are, after all, Chinese.