Most Ponzi schemes collapse relatively quickly, but there is fragmentary evidence that Mr. Madoff’s scheme may have lasted for years or even decades. A Boston whistle-blower has claimed that he tried to alert the S.E.C. to the scheme as early as 1999, and the weekly newspaper Barron’s raised questions about Mr. Madoff’s returns and strategy in 2001, although it did not accuse him of wrongdoing.

Investors may have been duped because Mr. Madoff sent detailed brokerage statements to investors whose money he managed, sometimes reporting hundreds of individual stock trades per month. Investors who asked for their money back could have it returned within days. And while typical Ponzi schemes promise very high returns, Mr. Madoff’s promised returns were relatively realistic  about 10 percent a year  though they were unrealistically steady.

Mr. Madoff was not running an actual hedge fund, but instead managing accounts for investors inside his own securities firm. The difference, though seemingly minor, is crucial. Hedge funds typically hold their portfolios at banks and brokerage firms like JPMorgan Chase and Goldman Sachs. Outside auditors can check with those banks and brokerage firms to make sure the funds exist.

But because he had his own securities firm, Mr. Madoff kept custody over his clients’ accounts and processed all their stock trades himself. His only check appears to have been Friehling & Horowitz, a tiny auditing firm based in New City, N.Y. Wealthy individuals and other money managers entrusted billions of dollars to funds that in turn invested in his firm, based on his reputation and reported returns.

Victims of the scam included gray-haired grandmothers in Florida, investment companies in London, and charities and universities across the United States. The Wilpon family, the main owners of the New York Mets, and Yeshiva University both confirmed that they had invested with Mr. Madoff, and a Jewish charity in Massachusetts said it would lay off its five employees and close after losing nearly all of its $7 million endowment. Other investors included prominent Jewish families in New York and Florida.

On Friday afternoon, investors and lawyers for investors with Mr. Madoff packed Judge Louis L. Stanton’s courtroom at federal court in Manhattan, hoping to question lawyers for Mr. Madoff and the S.E.C. But a deputy for Judge Stanton canceled the hearing, leaving investors with few answers. Several investors said they were planning to file lawsuits against the firm in the hope of recovering some money.

Based on the vagueness of the complaints against Mr. Madoff, his confession, as detailed in court filings, seems to have taken the F.B.I. and S.E.C. by surprise. Investigators have not explained when they believe the fraud began, how much money was ultimately lost and whether Mr. Madoff lost investors’ money in the markets, spent it, or both. It is not even clear whether Mr. Madoff actually made any of the trades he reported to investors.