Representatives of bondholders with some $28 billion in General Motors Corp debt have outlined specific proposals to the automaker on how to swap the debt for equity in a restructured company, a person with knowledge of the talks said on Monday.

GM has not yet accepted the proposals, the source said.

The debt swap is a crucial element in a revised restructuring plan for GM, which has received $9.4 billion in U.S. government aid and had been pledged $4 billion more as soon as this week.

Since Sunday, GM has also made significant progress in its talks with both bondholders and the United Auto Workers union, a second person familiar with the talks said.

GM faces a deadline of Tuesday to submit a new restructuring plan to U.S. officials demonstrating how it can be made viable after reducing debt and slashing costs.

Neither of the sources wanted to be identified because of the confidential nature of the negotiations intended to keep the top U.S. automaker from bankruptcy. But both said it appeared that GM would be able to detail progress in both sets of high-stakes talks to U.S. officials by Tuesday.

The more people have reason to fear the abyss, the less reason they have to go into it, the first person said.

In broad terms, the proposed terms of the deal to swap GM debt for equity in a recapitalized automaker would penalize any investors who hold out if a set percentage of other debtholders were to tender to join the deal.

That could be accomplished by leaving GM debtholders who choose not to participate in the deal with less senior claims and lower risk-adjusted returns.

It would also address a central criticism of the government-led recapitalization of GM-affiliated finance company GMAC and the so-called problem of free riders -- bondholders who wait in the hope that other participants will accept reduced claims so they can be paid back more fully.

In the case of GMAC, bond investor PIMCO turned down a debt-exchange offer during GMAC's now-completed $38-billion debt swap in late December, a move that was seen as threatening the deal.

Despite the defection, the U.S. Treasury moved ahead with a $5 billion equity injection into GMAC in late December.

The GM debt-exchange framework is intended to keep bondholders from bolting in a similar way. It also addresses a key concern about fairness in the parallel debt-reduction deal that GM has been negotiating with the UAW, the first person with knowledge of the talks said.

Detailed terms of the proposals including how much debtholders would be paid out were not immediately available. GM faces a government-set target of cutting the $28 billion held by bondholders by two-thirds.

The UAW is being pressed to accept just over $10 billion of the $20 billion it is owed for a retiree health care trust fund in GM stock under the restructuring.

Union negotiators have raised the concern that none of its retirees would be able to opt out of any revised terms for funding a health care trust fund .

That gives union workers less room to act than bondholders at GM who remain free to make individual decisions on whether to accept the debt-exchange, the person with knowledge of the talks said.

But by encouraging a high degree of participation, the proposed bond would look to level the playing field for the union as well, the person said.

GM is also talking to union officials about ways to cut costs, reduce payrolls and shutter surplus plants, people familiar with the talks have said.

(Editing by Christian Wiessner)