Arlington County police are seeking three men they say impersonated police in unrelated cases last week, including one home-invasion robbery in which a family was held at knifepoint.

The first incident happened about 11:20 p.m. Feb. 23 in the 300 block of South Fillmore Street. Two suspects banged on the front door of a house, said “police” and held up a piece of paper purported to be a search warrant, authorities said.

When the homeowner opened the door, the robbers pushed their way in, said Dustin Sternbeck, an Arlington police spokesman.

One robber held the woman and her two children at knifepoint on the living room couch, Sternbeck said. The other, armed with a gun, searched the house. Nobody was injured, Sternbeck said, but the men made off with almost $13,000 in cash and jewelry.

Police describe the suspects: One man was about 6-foot-3 and wore a ski mask, sunglasses, gloves and a winter coat; the other man was about 5-foot-5, had a heavy build and wore eyeglasses.

The second incident happened the next day in the 3700 block of Lee Highway. A man in a black convertible Ford Mustang pulled up beside a man idling at a red light, identified himself as a police officer and accused the driver of speeding.

“He said: ‘You’ve been speeding. I’ve been following you, and you need to pull over,’ ” Sternbeck said.

The victim pulled into a parking lot, and the impersonator, who was not wearing a uniform, demanded his driver’s license and registration.

When the victim, 70, pulled out his wallet, the impersonator walked back to his Mustang with it. After the man returned the wallet and drove off, Sternbeck said, the victim realized he was missing $160.

The suspect in that case is described as standing about 5-foot-9 and having an average build.

Police do not believe the incidents are related because of the types of crimes and the descriptions of the robbers.

Arlington police said residents can ask for an officer’s badge and badge number when they are pulled over. Residents who think they are in danger should call 911, police said.