The deal they said was so costly that neither side could afford to back out has collapsed, leaving at least $4 billion of now worthless investment on both sides of the Atlantic.

Involved was a daring endeavor desgined to pioneer high technology and bring liquefied natural gas from Algeria to the energy-poor East Coast of the United States.

Both the Algerian and American governments, which were ultimately responsible for the collapse of the 11-year-old effort, appear satisfied with the seemingly final breakdown of talks, although an insider described it as a "real disaster -- much crazier than it sounds."

Nonetheless, the U.S. government seems delighted at having drawn the line against the Algerian-championed new world economic order and what the Reagan administration sees as unwarranted demands on free-market mechanisms.

Algeria has said it prefers to keep the gas underground if it cannot win in its drive for price parity between the calorie value of natural gas and that of oil.

The losers are:

Algeria, which has $2.5 billion invested in pipelines, wells and liquefaction plants that specialists estimate cannot be fully used for another three or four years for want of expensive equipment in an alternative receiving country. The cost is estimated at $3 million a day in lost revenues.

The El Paso Natural Gas Co., which wrote off an investment of $365 million in gas-processing equipment and whose chairman, Travis H. Petty, has told his stockholders that further talks hold out little, if any, hope of a satisfactory settlement.

U.S. consumers, including Washington-area residents, in more than a dozen East Coast states who will pay for the $400 million regasification terminals at Cove Point in Maryland.

Back in 1969, when the deal first was rumored, Algeria was to sell 10 billion cubic feet of liquefied natural gas to El Paso annually for 25 years.

The deal then was not particuarly attractive for Algeria, which was to be paid only 30.5 cents per 1,000 cubic feet. That barely covered Algerian amortization costs, but it promised to give Algeria a head start in then fledgling liquefied natural gas technology, train personnel and provide associated opportunites for Algerian industry.

Furthermore, it was better than continuing the common practice of burning off natural gas produced during oil drilling since the enormous reserves of gas that promise to be Algeria's ace in the hole after its dwindling oil reserves give out toward the end of the century.

As oil prices soared in the 1970s, natural gas prices also rose, providing a potentially big source of income.

But after longtime Algerian president Houari Boumediene's death in december 1978, the new people at the Energy Ministry abruptly radicalized price policy, introducing the demand for parity with oil, based on the relative heating capacities. That would have meant a price of about $7 per 1,000 cubic feet of gas.

Despites expert's insistence that special tankers to carry the super-cold liquefied natural gas were 10 times more expensive than crude oil tankers and that the transport and handling costs were from six to seven times those of crude oil, the Algerians refused to take these factors into account.

The United States insisted that the cost of liquefied natural gas delivered to its shores be competitive with other alternative fuels and sources of supply on the U.S. market. Specifically, the United States feared that granting anything close to Algeria's demand of $7 per 1,000 cubic feet would only encourage a leapfrogging effect by Canada, which supplies three times as much gas through pipelines at $4.94.

Although the Carter administration was reliably reported to have been willing to favor a slight edge for Algerian gas, the Reagan team backed away from that stand at the final negotiating session on Feb. 18 in Algiers. By all accounts here, the U.S. team broke off the talks.

Why the Algerians, who so forcefully urged Iran to release the U.S. Embassy hostages before the Reagan administration took office, failed to apply the same logic to the gas deal is unclear.

But more than one energy specialist here is convinced that the Algerian negotiators must be asking themselves that question. One possibile explanation, which the Algerians strongly deny, is that they counted on some American generosity on the gas prices because of their crucial role in negotiating the release of the hostages.

For now, U.S. claims of victory are not without foundation. Oil and gas are in ready supply, largely because of the world recession. But experience shows that gluts are short-lived and in any case that United States imports only 5 percent of its natural gas needs compared with half its oil.

The Algerians are able to absorb the gas revenue losses because they get premium prices paid for their light, polluton-free oil, half of it sold to the United States.

"It's the old story of greed on one side," one specialist said, "and a political slap in the face on the other.

A Western European diplomat said: "The El Pasa deal would have committed Algeria and the United States to two decades of commercial collaboration with all the potential industrial and political spinoff that could entail."

There are indications, however, that perhaps such close potential political collaboration would have been as distasteful to revolutionary Algeria as the more practical consequences of the deal were to the Reagan administration.

Other observers suggest that energy-poor Western Europe is a more natural market for Algeria. It needs the gas more and is nearer, thus reducing transportation costs. Some Western European countries already have negotiated gas purchase from Algeria.