Americans who illegally download songs and movies may soon be in for a surprise: They will be warned to stop, and if they don’t, they could find their Internet access slowing to a crawl.

After years of negotiations with Hollywood and the music industry, the nation’s top Internet providers have agreed to a systematic approach to identifying customers suspected of digital copyright infringement and then alerting them via e-mail or other means.

Under the new process, which was announced Thursday, several warnings would be issued, with progressively harsher consequences if the initial cautions were ignored.

The companies took pains to say that the agreement did not oblige Internet providers to shut down a repeat offender’s account, and that the system of alerts was meant to be “educational.” But they noted that carriers would retain their right to cut off any user who violated their terms of service.