The first of the two deaths was that of Shawn Robert Lohrman, 24, of Ell Street, Greeneville.
Lohrman, according to the Tennessee Highway Patrol (THP), died early Saturday as the result of a motorcycle crash on Chuckey Highway.
The second traffic death was that of Donald Ray "Donnie" Nelson, 47, of Martin Road, Limestone.
Nelson died after he was thrown from and run over by a farm tractor he was using to tow a hay wagon along Old Stage Road in eastern Greene County about 7 p.m. Sunday.
The first of the two fatal accidents was reported to the Highway Patrol about 3:30 a.m. Saturday, according to a THP dispatcher, who said Trooper Mark Higgs was dispatched to Chuckey Highway near Chuckey Elementary School in response to a report of a serious motorcycle crash there.
The THP dispatcher said officers are unsure exactly when the fatal crash took place, but a passerby reportedly discovered the wreck about 3:15 a.m.
Higgs' initial report on the early morning, single-vehicle crash indicated that Shawn Robert Lohrman had been riding a 1990 Suzuki motorcycle south on Chuckey Highway when he lost control of the vehicle in a curve.
The motorcycle traveled off the right side of the road and struck a guardrail, according to the THP report, which noted that Lohrman was thrown from the motorcycle.
Lohrman was wearing a helmet, but still sustained fatal injuries, according to the THP.
He was pronounced dead at the scene.
The second traffic fatality of the weekend was reported at 7:09 p.m. Sunday, according to a report filed by Deputy Sheriff Joe Jaynes.
Witnesses, according to Jaynes' report, said the fatal accident took place when a farm tractor being used by Donald Ray Nelson to tow a hay wagon began swerving from side to side in the 9200 block of Old Stage Road, causing the driver to lose control.
The tractor and its trailer eventually turned sideways, causing Nelson to be thrown from the tractor's seat and subsequently run over by the vehicle he had been driving, according to Jaynes' report.
A Greene County-Greeneville Emergency Medical Services ambulance responded to the scene and transported Nelson to Laughlin Memorial Hospital, where he died, according to Jaynes' report.
Also responding to the crash scene were units of the Limestone Volunteer Fire Department from Washington County, according to the the Sheriff's Department report.