Hackers have repeatedly penetrated the computer network of the company that runs the Nasdaq Stock Market during the past year, and federal investigators are trying to identify the perpetrators and their purpose, according to people familiar with the matter.

The exchange's trading platform—the part of the system that executes trades—wasn't compromised, these people said. However, it couldn't be determined which other parts of Nasdaq's computer network were accessed.

Investigators are considering a range of possible motives, including unlawful financial gain, theft of trade secrets and a national-security threat designed to damage the exchange.

The Nasdaq situation has set off alarms within the government because of the exchange's critical role, which officials put right up with power companies and air-traffic-control operations, all part of the nation's basic infrastructure. Other infrastructure components have been compromised in the past, including a case in which hackers planted potentially disruptive software programs in the U.S. electrical grid, according to current and former national-security officials.

"So far, [the perpetrators] appear to have just been looking around," said one person involved in the Nasdaq matter. Another person familiar with the case said the incidents were, for a computer network, the equivalent of someone sneaking into a house and walking around but—apparently, so far—not taking or tampering with anything.