While prostitution is legal in France, the investigating magistrates are trying to determine whether the women were paid with funds one of the men might have embezzled. The magistrates seek to discover whether Mr. Strauss-Kahn might have known of any such payments.

Eight people have been charged in the case, including a prominent lawyer, a local police official in Lille and three executives of the Hotel Carlton there.

Mr. Strauss-Kahn has denied complicity in prostitution and made no comment to reporters as he arrived at the Lille police station on Tuesday. It was not clear whether his overnight detention was routine, or whether information had emerged in the course of the first day of questioning that had prompted the move. French law allows a person to be detained for questioning without charge for 48 hours, with a possible extension to 48 hours in the most serious cases.

Last May, Mr. Strauss-Kahn resigned as the managing director of the International Monetary Fund and lost any hope of becoming his party’s presidential candidate after he was indicted on attempted rape and other charges involving a housekeeper at a New York hotel. The case was dismissed after prosecutors questioned his accuser’s reliability as a witness, but he eventually admitted that his encounter with her had been “an error” and “a moral failure.”