Employees with an ax to grind are increasingly using Internet cloud services and other computer tools to hack their current or former companies, according to the Federal Bureau of Investigation and Homeland Security Department.

The workers use services like Dropbox Inc.’s cloud storage or software that lets them gain remote access to corporate networks in order to steal trade secrets and other data, the agencies said in a public service notice on a government website recently. Companies victimized by current or former employees incur costs “from $5,000 to $3 million,” the agencies said without naming specific companies or incidents.

The thefts have “resulted in several significant FBI investigations” in which individuals used their access to destroy or steal data, obtain customer information and commit fraud using customer accounts, according to the notice. The alert comes as Home Depot Inc. and JPMorgan Chase & Co. have confronted hacking attacks suspected of coming from outside the companies and shows that companies need to be alert to insider threats.

“While corporations devote significant resources to protecting against external threats, managers must also remain aware of the potential damage that can be caused from within by employees intent on causing harm to network systems,” an FBI spokesman, Joshua Campbell, said in a statement.

The hacking also can give an individual a competitive advantage at a new company, according to the alert.

“Multiple incidents were reported in which disgruntled or former employees attempted to extort their employer for financial gain by modifying and restricting access to company websites, disabling content management system functions, and conducting distributed denial of service attacks,” the agencies said.