House and Senate negotiators said that they had reached an agreement yesterday on a bill that would save companies an estimated $80 billion in pension contributions over the next two years. Airlines and steel companies, which have some of the weakest pension plans, would get an additional break, worth about $1.6 billion.

The measure offers all employers with pension plans a break by changing the way they calculate, in today's dollars, the value of the benefits that they must pay in the future. The new method will make their future pension obligations look smaller. That, in turn, means they will not have to set aside as much money today.

A second provision offers relief to the major airlines and to steel companies. Their pension funds are so badly eroded that they are becoming subject to a special set of funding rules, under which companies with very unhealthy pension plans have to make large quarterly contributions to revive them. As currently written, the bill would allow the airlines and steel companies to pay only 20 percent of what they would otherwise owe in these special catch-up contributions.

The major airlines are expected to save about $1.3 billion in pension contributions over the next two years if the measure becomes law. Steel companies that still operate pension funds would save about $300 million.

United Airlines stands to benefit more than any other company. It has been operating under bankruptcy court protection for more than a year, and has said that the cash demands of its pension plans are the biggest obstacle to its successful reorganization. United, a unit of the UAL Corporation, disclosed late last year that it must contribute about $4.8 billion to its various employees' pension funds by 2008, much of it this year and next.

United has already asked the Internal Revenue Service, which regulates pension funds, for permission to defer some of these contributions. But the I.R.S. has not yet acted on its unusually extensive request.

If the current legislation is enacted, much of the pressure will be off United, at least for two years. If United's pension funds do not recover by then, the special contributions will come due.

The bill is still subject to passage by each house of Congress before it could be signed into law by President Bush. It is widely expected to pass in the House of Representatives, possibly today, before the House begins a two-week recess. But it could still run into trouble next week in the Senate, where Democrats, led by Senator Edward M. Kennedy, have been threatening to block or delay it.

Senator Kennedy said yesterday that he opposed the current version of the bill because it would give a pension break to a few large corporations, while denying relief to many small, unionized companies that also have big pension bills coming due.

A delay could be painful to many of the companies that offer pensions to their workers. Congress is working against a deadline. If the measure is not enacted in the next two weeks, an unknown number of additional companies will be required to make the special contributions to their pension funds that the airlines and steel companies owe. The payments come due on April 15. Current, detailed information about the health of individual pension funds is not public information, and officials working on the pension measure have not identified the companies in this predicament.

Congress has been grappling for more than a year for an acceptable way to help companies keep their pension funds legal. Agreement has been elusive, and some companies with enough cash have gone ahead and made large pension contributions voluntarily.

Companies have lobbied forcefully for relief, arguing that the market conditions of the last few years were unusual and that easing the funding rules would merely tide them over and not endanger their pension funds over the long term.

The Bush administration, as well as some lawmakers and companies, have, however, opposed a relaxation of the pension rules. They have argued that easing the rules on funding might lead companies to use money earmarked for pensions to run their businesses. Some pension funds could then collapse, and the federal government would be stuck with the tab. The federal government insures pension benefits up to certain levels.

Airline employees, especially pilots, have a lot to lose if that were to happen. Pilots at major airlines have been promised generous pensions, and if their pension funds failed and were taken over by the government, some pilots could lose benefits worth hundreds of thousands of dollars. The more insolvent the plan, the greater the potential losses.

The union that represents the pilots of most major airlines has nevertheless supported the special relief measure, apparently considering it important for the industry to survive and thrive.

Opponents of pension relief have also argued that it would constitute an unfair subsidy to companies that have let their pension funds deteriorate.

"This money is being given to one competitor, with no strings attached, to attack another competitor," said Edward Faberman, a lawyer who represents the Air Carrier Association of America, a group of low-fare airlines that opposes the pension break to the major carriers.

Airlines opposed to the break include AirTran, Frontier, Spirit, America West and JetBlue, although America West and JetBlue are not members of the association.

A United spokeswoman, Jean Medina, said the airline was "optimistic" about the bill's chances. United has not disclosed more detailed information about how much relief the legislation would provide.

Pension specialists have also warned that relaxing the funding rules for individual industries - the airlines and steel companies - would set a precedent that other companies would invoke in the future, if their own pension plans ran into trouble.

The White House had threatened to veto any measure that extended overly broad relief to companies, but certain provisions that caused the most concern were deleted from the current version. Administration officials expressed satisfaction in the bill as written yesterday.

Low interest rates can cause great trouble for pension plans, as current conditions demonstrate. Interest rates are used in pension calculations as a proxy for the speed at which a pension fund will grow; low rates therefore translate into large future obligations, meaning companies must set aside more money today.

Currently, the federal pension rules require companies to use a rate linked to the 30-year Treasury bond, which is very low, in their calculations. The bill would allow them to change to a corporate bond rate, which would be higher. Using the higher rate in their calculations, all companies would see the value of their future pension obligations shrink.

This provision would have no effect on the size of the pensions that retirees actually receive.

Earlier, the administration sought more rigorous funding rules for all companies that offer traditional defined-benefit pensions. But those goals proved overly ambitious as many companies were struggling to comply with the current rules because of difficult interest rate and market conditions.

Micheline Maynard contributed reporting for this article.