In his last letter to his parents from South America, Timothy G. Welch wrote that he and his girlfriend, Joyce Holmes, were buying a dugout canoe and planning to paddle 125 miles down a jungle river to the tiny port town of La Tagua in the Colombian interior.

"We plan to start down the river sometime tomorrow," he wrote. "They say it'll take us a week, but I think we're a little slower than they think."

That was Feb. 17. Welch and Holmes, both 25, haven't been heard from since, although they had written regularly to friends and family before that and indicated that they would keep in touch.

By early May, Welch's parents, who live in Falls Church, were so frantic that they set off on a fantastic and dangerous odyssey of their own into the jungle to find "the kids," as they call Tim and Joyce. In two heartbreaking months and with the aid of padres and peasants they combed 600 miles of river valleys in one of the most unforgiving and lawless regions of the hemisphere.

They found a world of lazy river villages and rough farmland carved out of a vast wilderness, a world peopled by subsistence farmers, Indians, bush pilots, missionaries and soldiers. But while people seemed friendly and concerned, the parents found no kids and only faint traces of their passage.

Often they heard rumors that Tim and Joyce had been sighted, but just as often these turned out to be maddeningly wrong. The last reliable trace they found placed the pair in the river town of Puerto Leguizamo, on the Peruvian border, in mid-March, meaning they probably completed their canoe trip successfully and were looking for new adventures.

But after Puerto Leguizamo, the trail ran out.

"We stopped at every military post, every village, every house, every Indian tribe. We just covered that thing fro one end to another and nobody had ever seen 'em" along a stretch of river they might have taken from Puerto Leguizamo, said George I. Welch, a retired government physicist who is fluent in Spanish. Welch plans to continue searching, and possibly make another trip. Joyce's parents live in Long Beach, Calif.

The Welches met Tim and Joyce in the town of Popayan on Feb. 5 for a joint holiday and traveled by bus to San Agustin, where the Welches left them on Feb. 10 poring over maps and making plans. The Welches spent some more time in nearby Ecuador where they received Tim's Feb. 17 letter, then returned to Falls Church, where they wondered why another letter wasn't waiting for them.

The Welches have been in touch with the U.S. State Department and with the Colombian and Peruvian embassies here, all to no avail.

A State Department spokesman said the Privacy Act prohibited comment on the case. He said the department tries in a limited way to help find missing Americans in foreign lands, but added, "We do not have the capacity to actually mount a search in the way an American law enforcement agency could here. We're not in a position to hit the streets and knock on doors." According to friends and relatives, Tim is a charming, unconventional, adventuresome youth with a slightly radical political bent and a yen for travel that hs taken him on trips across the United States, through Central America and on one hair-raising three-month jaunt around the Caribbean in a leaky 21-foot sailboat with a cracked mast.

Before the trip, Tim worked as a paralegal for Pine Tree Legal Assistance, Inc., an organization in Maine which aids the poor. He left after tiring of the nine-to-five routine, friends said. Earlier, his parents said, Tim was graduated from Swarthmore College in Pennsylvania.

Peter Frederick, a college friend, described Tim as "the original vagabond. He could go just about anywhere and do anything . . . on almost no money."

"Tim's a real adventuresome type," said Jeffrey Pennington, a former girlfriend who took many trips with him ". . . He sort of ignores the walls of convention. He doesn't see that things have to be done in any one way." Pennington recalled that Tim repaired their old '55 Chevy on one trip to Mexico, making his own tools from scraps they found along the road.

Pennington had been to Colombia on an earlier trip, and said that later she gave Tim a copy of her travel notes, which showed how one could go by canoe from Florencia down the Orteguaya River -- which is exactly what Time said in his last letter that he and Joyce were planning to do.

"He really likes to test himself and other people in situations to see what the limits are," said Timothy's sister, Katharine, now a law editor in Charlottesville, Va. "I think that has a lot to do with what this trip's about."

It was Katharine who introduced her brother to Joyce Holmes last August in Atlanta, where the two women were living in the same apartment building. "I knew this was the kind of woman for Tim," Katharine said. "She had a huge map of the world on her living-room wall. She likes cars and she likes travel."

Orginally, Katharine was planning to go on the trip, too, but said she backed out after it appeared that her brother was seriously planning to ravel down a river by canoe. Tim and Katharine had talked and corresponded for a long time on a proposed trip to South America. In one letter, she recalled, Tim had fantasized about the terror of going down the Amazon at flood time in a canoe, then finally reaching calm waters.

"For the rest of our lives," he wrote, "when things aren't quite right we can think about when they were a lot worse and know that the placid lake always comes. When we remember grappling with the fundamental challenges of life and death in a tropical jungle we are able to maintain a better perspective . . ."

Joyce Holmes, according to her father, a chemical engineer in California, has been "a traveler and a hiker all her life. . . As a family, we have backpacked in the Sierras, and real regularly." William H. Holmes said his daughter is "always ready to explore."

Her mother, lapsing into the past tense at the end of a telephone interview, said Joyce "was a happy girl most of her life. She was our little billy goat on our hikes, she loved to scamper up the hills, loves to swim, just an active, happy person and very interested in people."

Joyce's passion is photography. She graduated from a California school specializing in that subject, her parents said. Friends and relatives said that she probably carried more than $1,000 in photographic equipment and film on the Colombian trip. In addition, Timothy's family thinks the pair may have carried that much again in U.S. green cash -- not much for an elaborate, lengthy trip but a fortune, they concede, in the eyes of a South American peasant who might contemplate robbery.

George Welch tends to discount the possibility of robbery. "They might have got ripped off somewhere and are trying to work their way out," he speculated. "They do rip people off, but it would be very rare that they would kill them."

While friends and relatives for the most part described Tim as an experienced and adept traveler who did political and other research in advance of his trips and was wary of possible wrongdoers, the dangers of this Colombian jungle trip were worthy of "Raiders of the Lost Ark."

For one thing, the Putumayo Territory in Colombia where the Welches think Timothy and Joyce were last seen in mid-March was the scene at that same time of a military operation in which thousands of government troops killed and captured virtually the entire high command of M19, an antigovernment band of leftists that had become South America's most famous active guerrilla movement.

Tim's last letter said that from Puerto Leguizamo -- the border town which the parents think Tim and Joyce did in fact reach and were last seen in -- they might "get on a barge going upstream and get off somewhere in southern Colombia" -- a route that could have put them near or even in the military operation.

Just before the operation, on March 11, 300 M19 guerrillas raided the nearby provincial town of Mocoa, killing the police chief and kidnaping the assistant mayor. On March 7, the guerrillas hd killed kidnaped American Bible translator Chester Allen Bitterman after accusing him of being a CIA spy.

Beyond political problems that the young American travelers could have stumbled upon in the shaky democracy, drug traffic is rife there. Colombia is one of the biggest marijuana exporters in the world. Tim's relatives and friends all said the traveling youths were determined not to become involved with drugs in any way on the trip.

In addition to drugs, the Colombian border region with Peru and Ecuador where Tim and Joyce were last seen is a hotbed of smuggling of all kinds -- and smugglers can be very touchy if one happens upon them in the jungle.

Finally there are natural dangers -- swift rivers containing man-eating piranha fish and jungles with 20-foot anaconda snakes that can crush and then swallow a man whole.

Welch described his son as "prudent" and said, "These kids are very responsible." He also said his son's Spanish is "quite good."

But Frederick, Tim's college friend who helped him prepare for the earlier dangerous Caribbean sailboat trip, painted a different picture:

"There's a thousand ways I can imagine him being totally unprepared for what's about to happen. When he wanted to, he could talk his way out of things, but he didn't speak Spanish very well. He could ask where the bathroom was, but wasn't really fluent."

Frederick said Tim asked him to go on the trip but Frederick turned him down. "It sounded like a typical Tim Welch trip. It was underprepared. It didn't sound like he knew where he was going real well. He was going with his girlfriend and neither of them spoke Spanish. Neither of them had been to the area at all. They were going without a guide. . . I'm sure when he left the states that he didn't know that that area had a lot of guerrilla activity going on."

The Welches hope they may still find Tim and Joyce. Welch talks now of a trip to Peru, of inquiries through official channels.

"We've still got quite a few things going," he said, "but I don't know if we're going to have any luck or not." He shook his head. "Boy, it's sure been a long time."