Chip East/Reuters

Two rival bids for Dell Inc. have emerged, threatening to complicate or change — or upend — an effort to take the embattled computer maker private in a $24 billion deal under the leadership of Michael S. Dell.

The private equity giant Blackstone Group and the investor Carl C. Icahn have each separately submitted preliminary takeover proposals before a deadline set by a special committee of Dell’s board intended to drum up other offers, people who had been briefed on the matter but were not authorized to speak publicly said.

Both proposals are valued at more than the offer of $13.65 a share by Mr. Dell and his private equity partner, Silver Lake.

The Dell committee may announce Monday whether it believes either bid is likely to lead to a superior offer, one of the people briefed on the matter said.

But much work remains for Dell’s special committee and the two new bidders. Both of the new proposals are highly preliminary, meant to keep talks going after the 45-day so-called go-shop period.

Neither proposal has firm financing lined up, instead relying on “highly confident” letters from their banks that they can raise the money. Blackstone and its group are working with Morgan Stanley, while Mr. Icahn, who has also built a substantial stake in Dell, is using the Jefferies Group. That means that a final bid from either suitor is weeks away. And Dell’s special committee must also determine whether any such proposal would be superior to the all-cash offer by Mr. Dell and Silver Lake.

Mark Lennihan/Associated Press

Nonetheless, the emergence of two competing bids is a surprising setback to the buyout effort. Few would have predicted Dell, a struggling personal computer maker, would have attracted so much interest when Mr. Dell and Silver Lake announced their takeover offer early last month. Analysts and investors had widely believed that Mr. Dell, who founded the company that bears his name nearly 29 years ago in his college dormitory, would prevail.

At the least, the preliminary bids may lead to a higher offer for Dell shareholders, some of whom have vocally opposed the current bid as undervaluing the company.

Strictly speaking, neither Blackstone nor Mr. Icahn would take Dell completely private, unlike the bid by Mr. Dell and Silver Lake. Both envision leaving part of the company public through what is known as a stub, which would allow current shareholders to keep a stake.

Blackstone proposed paying more than $14.25 a share, working with two technology-focused investment firms, Francisco Partners and Insight Venture Partners. While the private equity firm did not specify what percentage of Dell would remain public, it proposed letting shareholders sell their entire holdings if so desired. Blackstone has also weighed selling part of Dell’s business, like its financial arm, to help pay for any deal.

Mr. Icahn outlined a plan to pay $15 a share for about 58 percent of the company, meaning that other investors would be allowed to sell only part of their stakes.

Should the special Dell committee choose an offer from either suitor, Mr. Dell and Silver Lake would have just one chance to match or top that bid.

The appearance of Blackstone as a potential spoiler is one of the few times that a private equity firm has “jumped” another’s deal. Blackstone and others in the private equity industry are fighting off an antitrust lawsuit in the Federal District Court in Boston that cites this apparent industry custom as evidence of collusion.

The appearance of Blackstone and Mr. Icahn was also one of the rare instances when a go-shop period actually attracted another suitor. By one deal maker’s reckoning, fewer than 20 percent of these efforts for a deal worth more than $1 billion have found an alternative offer.

Letting some shareholders remain invested in Dell could go a long way toward appeasing one of the most vocal critics of the current deal: Southeastern Asset Management, the company’s biggest outside investor, with a stake of about 8.4 percent. Southeastern has declared publicly that it will not accept Mr. Dell’s offer, and floated the idea of a public stub.

Blackstone has spoken with Southeastern, people briefed on the matter said.

Mr. Icahn, who disclosed in a letter last Friday to the Dell special committee that he owns 80 million shares, or less than 5 percent of the company, had previously told the committee that he opposed Mr. Dell’s current bid. Neither Mr. Icahn nor Blackstone offered specifics about how they would run Dell after the deal is completed. While Mr. Dell has committed to negotiating with any party that the special board committee deems likely to produce a superior proposal, he is free to leave his post as chief executive.

Blackstone has approached possible replacements for Mr. Dell. But at least one of them, Oracle’s president, Mark V. Hurd, has expressed little interest.

Blackstone and Mr. Icahn could also have difficulty financing their offers. Mr. Dell and Silver Lake have lined up five major lenders to support their bid. It is not clear whether any banks would support a higher-priced offer that would lay more debt onto a company whose business is widely seen as deteriorating.

Another factor the special Dell committee must weigh is the cost of leaving some Dell shares publicly traded on the Nasdaq stock market. Underlying the premise of Mr. Dell’s bid is his contention that the changes needed to fix the company would upset public shareholders, further hurting its stock price.

Andrew Ross Sorkin contributed reporting.