Time is running out for U.S. securities regulators to file civil charges for alleged wrongdoing during the financial crisis.

Federal laws under which the Securities and Exchange Commission usually goes after alleged fraud and other misdeeds have a five-year statute of limitations. The five-year limit is causing SEC officials to race to file lawsuits in some cases and ask lawyers representing the targets of certain investigations to give the agency more time, according to people close to the investigation.

The...