ATLANTA — The federal authorities are investigating whether three recent attacks against the power grid in Arkansas are linked, and utility officials have asked residents to remain alert to the threat of more trouble.

The Federal Bureau of Investigation said that two power poles in Lonoke County, just east of Little Rock, were deliberately severed early on Sunday. The authorities said that a stolen tractor, which had an extendable arm with a circular saw blade at its tip, was used to take down one of the poles.

The incident came more than six weeks after the F.B.I. opened an inquiry into a report by Entergy Arkansas, a utility company, that one of its high-voltage transmission lines had been brought down in Lonoke County. Investigators said someone had fastened a cable to the 100-foot transmission tower and laid it across a nearby railroad track in what the F.B.I. described as “an attempt to utilize a moving train to bring down the tower.”

Investigators recovered the cable, which was a half-inch in diameter and attached to a 15-inch eye bolt, at the scene in Cabot, a city of about 24,000 people.