Remembering my own many unsuccessful requests for a visa to China, I watched skeptically as my parents, Tom and Frances Mathews of San Mateo, Calif., walked unannounced into the China Travel Service office here and asked to go to Canton.

"How about next Saturday?" the young Chinese travel agent said. My jaw dropped. Tourism was catching up with Maoism.

Even after 1971's Ping-Pong diplomacy made American travel to China possible, U.S. citizens have had to scheme and beg for months or years to get a treasured China visa. Most have only been able to go under the guise of "special interest" groups studying health care or rice farming, rather than as carefree tourists.

No longer. Many prospective China travelers back in the States are still adding their names to long waiting lists for a few U.S. organized tour groups. But Americans who happened to be in Hong Kong in recent weeks have found that a quick and, by all accounts, delightful trip to China is almost as easy to arrange as a visit to one of the local tailors.

The official China Travel Service, with help from a few private Hong Kong travel agencies, has been granting visas on only two or three days notice to nearly anyone interested in a four-day, three-night tour of nearby Canton and the surrounding countryside. The Chinese are experimenting with what may be a much more ambitious program and so far have forbidden newspaper advertising. Their secret has been well enough kept that the Canton weekend tour has yet to be fully booked, although longer and less frequent tours to Kweilin and to Peking have built up waiting lists at least through June.

My parents heard of the tour by word of mouth, as did most of the 73 others in their Canton group, which included perhaps 40 Americans. My wife had called to tell them about the Canton offer while they were still packing for a long-planned trip here. When my mother passed on this news to her travel agent in San Mateo, three other agents called within hours for more information.

The Canton tours can take up to 150 people each weekend. No more than a third are supposed to be Americans, although some travel agents here say that quota is not rigidly enforced. As far as is known, no Americans have been turned away except those that the Chinese can clearly identify as journalists, diplomats or missionaries. Missionaries are barred, and journalists and diplomats usually must clear trips through the foreign ministry in Peking.

The weekend tour leaves every Saturday morning for a 90-mile railroad trip over the border to Canton.It returns from Canton Tuesday morning. The cost will increase to $180 per person this month, from a rate of $163 that was in effect for the first two months. That covers nearly everything - food and lodging at Canton's cavernous Tung Fang Hotel, transportation, guide service and evening entertainment.

Every tour group spends one day at a rural commune outside the city. They see and eat a delicious country meal. Another day is spent at a ceramic factory and an ancient temple in the smaller city of Foshan, north of Canton. Tour members usually see one evening ballet or acrobatic performance, visit the pandas at the Canton Zoo, and hear a brief lecture on the sins of imperialism at a spot where Chinese revolutionaries were cut down by British and French guns. "We all shook our heads sorrowfully," my mother said.

"Nobody in our group had more than a week's notice that they could get on such a trip," she said. "Many people were sending wires to friends who were expecting them elsewhere that weekend."

My parents walked into China Travel Service at 77 Queens Rd. Central in Hong Kong (the Kowloon branch is at 27 Nathan Rd.), filled out application forms in duplicate, left two photos each and a $44 deposit. They applied on a Friday, too late for the next day's tour but in plenty of time for the following Saturday. On Wednesday they joined other tour members for a briefing at the Miramar Hotel. China Travel Service officials took their passports and dispensed advice: "You cannot cash American Express or Citibank travelers checks in China," said tour guide Li Wai-Wing. "You can take exposed film out of the country if you don't take pictures of military installations."

Americans with Taiwan visas stamped on their passports had no trouble: The Chinese stamped their visa on a separate slip of paper and paperclipped it to the passport. Citizens of South Africa, Rhodesia, Israel and South Korea were supposedly barred, but two Rhodesians travelling with British passports got on the trip. Two Canadian Christian missionaries, after apparently claiming other more innocous occupations on their applications, also joined the tour. There was no word of what happened to the Chinese-language Bibles they brought, in with them.

After two decades of entertaining foreign trade-fair delegates twice a year, the citizens of Canton might be expected to be accustomed to Westerners walking their streets. But the Americans found themselves stared at wherever they went.

"When we got to the zoo they stopped watching the animals," my mother said.

For some that was one of the trips delights. For others it was the clash of cultures, or the sight of new ways being grafted onto old, that every visitor to China seems to discover in some different way. Strolling around a mid-city park, my father came upon the rare sight of a Chinese tennis team practice, with tall, well-trained young women mastering the capitalist art of rushing the net. Other tour members enjoyed explaining to an inquisitive hotel waiter what "B.Y.O.B." meant in the announcement of an impromptu tour group party pinned to the hotel bulletin board.

The low ebb of tourist travel to Hong Kong in cloudy mid-winter and China Travel Service's low profile have kept the Canton tours small so far. Perhaps it's just as well. Tour members found they had to eat, and sometimes sleep, in their coats in the chilly Tung Fang. Inexperienced guides sometimes failed to inform all tour members of where to get buses for evening performances. But better weather, better service and the travel grapevine may quickly fill up the weekend tours, which will be suspended from mid-April to mid-May for the spring trade fair.

A friend or relative in Hong Kong can make a preliminary booking: No reservations can be confirmed until the applicant has personally handed in his passport. People without other contacts in Hong Kong can write private travel agents such as Swire Travel Ltd., 9 Connaught Rd. C.; Travel Advisers Ltd., Peninsula Hotel, Kowloon; or Arrow Travel Agency, 2101 Alexander House, all in Hong Kong.