This winter, a little more than a year after the Europeans defied American sanctions, Soviet gas will begin flowing through the new pipeline to heat West European homes.
Few Europeans or Americans will notice the difference.
Although the arrival of American missiles may create new East-West tensions, trade with the Soviets is back to normal, and tensions between the United States and its allies over the commerce have lessened.
Spats over high-technology exports continue. But they are off the front pages , confined to a little-known, secrecy-obsessed organization called the Coordinating Committee for Export Control (Cocom).
At the same time, progress seems to have been made in resolving transatlantic differences. From the European perspective, the Reagan administration seems to have accepted that commercial links with the Soviets cannot be cut. From the US perspective, the Europeans have also made compromises, ending soft credits to the Soviets and restricting militarily sensitive exports.
''The United States took measures, then abandoned them, so now there is a certain serenity,'' explains Elizabeth Bukspun of the French Foreign Trade Ministry.
''The French attitude towards strategic technologies has become a bit more malleable,'' says a US diplomat.
This does not mean that the Europeans have converted into hard-line American-style believers in economic ''warfare.'' Politically, they continue to think that economic ties with the East cool tensions.
Exports to the East total only a small part of their trade. And experts at the Organization for Economic Cooperation and Development (OECD) do not expect these exports to grow very quickly in the next few years.
But with Europe recovering slowly and its traditional Middle Eastern and African markets slumping, the commerce retains an importance out of proportion to its size.
In France, for example, sales to the Soviet Union are crucial for the country's major engineering and construction firms. Technip reports that in 1982 it did almost 10 percent of its business with the Soviets. Creusot Loire admits it would have gone bankrupt if it did not have about $1 billion of work contracted on the gas pipeline.
''We want to keep our people working,'' says Bukspun at the Foreign Trade Ministry. ''The Soviet Union is a solvent market.''
It is no surprise, then, that the Europeans have launched an export campaign. Last year, they frantically competed to develop a gas field at Astrakhan in the Volga region. French firms, including Creusot and Technip, finally beat out German and Canadian competitors for contracts worth about $700 million. This year, the Europeans are bidding to develop another large Soviet gas field at Tengiz.
The Reagan administration worries that this competition translates into dependence on the Soviets - especially when imports as well as exports are considered. Soviet exports to the West rose by 10 percent during 1982 and 4 percent in the first half of this year. In Eastern Europe as a whole, exports increased by 4 percent - the first rise in three years.
With the construction of the new pipeline, European Community officials contacted in Brussels admit that by 1990, Russia will be Europe's No. 1 gas supplier.
Soviet oil exports are expected to decline, however, so deliveries at their peak will represent meet only 5 to 6 percent of Europe's energy needs. The Europeans argue that this level is not a threat.
''The Russians are an important supplier,'' admits Francois Lecorre of the French Foreign Trade Ministry. ''But they are not crucial. We could replace their supplies quickly.''
With the pipeline moving ahead on schedule and the Europeans scrambling to trade even more with the Soviets, how have the tensions over the commerce been toned down? Common interests, European and American officials say, were always stronger than the differences.
Take subsidized credits. The US goal has long been to end all such subsidies. But the Europeans feared sales to the Soviets would disappear without the lower rates.
After much haggling, an agreement on a ''consensus'' interest rate was reached at a fall meeting of the OECD. The French were able to keep some subsidies, but minimum financing for projects to the East was placed at just above 12 percent - a rate that satisfied the US.
Why did both sides compromise?
''If we hadn't, there would have been a credit war,'' explains Bukspun. ''We don't like the high interest rates, but such a war would have been bad for everyone.''
Progress also seems to have been made on the issue of high-technology exports. In principle, the Europeans have always agreed that the Soviet Union should be denied strategically valuable materials. In practice, though, the European definition of strategically valuable has been much looser than the American definition.
But the disagreements are less severe than before, diplomats close to the Cocom negotiations say. The US has realized that it cannot blacklist everything vaguely strategic, and that it must negotiate, not unilaterally impose sanctions.
Cocom's European members, meanwhile, have stiffened their checking procedures on high-technology exports. The French have instituted an interministerial checking procedure, and West German officials recently cooperated with the US to stop a shipment of computers Eastward.
''Outstanding issues remain,'' says a diplomat involved in the negotiations. ''But the general strategic concept is the same on both sides.''
Some tension within this general consensus will always exist. The Europeans' fear of Soviet power makes them amenable to controlling exports of sensitive materials. At the same time, forging strong commercial links with the East is in their interest.
The Europeans note, with smiles, that the same friction exists in the US.
''The reality is that America will also sell as much as it can to Russia,'' Bukspun says. ''Remember who lifted their own embargo because of internal political pressure? And who sold all that grain to Russia?''