According to a Florida Highway Patrol incident report we obtained ... the 35-year-old was pulled over on Oct. 10 in Tallahassee after allegedly going 78 MPH in a 55 -- while his two kids were in a 2023 KIA SUV with him.

One officer wrote in the report that after stopping the former NFL player ... he admitted to driving despite knowing he had a suspended license. The cop stated in the docs this is not the first time he's committed the offense.

In addition, the officer said he discovered during the stop Bradham had an active warrant for possession of a controlled substance out of Leon County.

The 35-year-old was ultimately thrown in handcuffs and taken to a nearby jail ... where he looked none too pleased to be posing for a mug shot. He was eventually released.

Court records show he's since been charged in Wakulla County with one felony count of driving while license suspended or revoked.

The incident is hardly Nigel's first run-in with the law. Back in 2021, he was arrested after cops said they found over three pounds of weed and guns in his Corvette.

Bradham was picked by the Bills in the fourth round of the 2012 NFL Draft. He later joined the Eagles in 2016 -- and helped them win a Super Bowl.