In the first, a car collided with a single decker that was stationary on the soutbound carriageway of the A9 near Murthly at 10:15 on Friday.
A 96-year old woman passenger in the car died. The driver, a woman in her 60s, suffered less severe injuries.
About an hour later a 78-year-old man was fatally injured when he was hit by a bus in Forfar.
He was taken to Ninewells Hospital, Dundee, after the accident in Don Street at 11:10, but died as a result of head injuries.
The earlier accident on the A9 involved a red Mazda CX5 and a white D&E Coaches bus.
A spokesman for Police Scotland said: "The bus was stopped in lane one of the southbound dual carriageway behind a second D&E Coaches bus at the time of the incident.
"Both the driver and passenger of the Mazda were taken to Ninewells Hospital, where sadly the passenger, a 96- year-old woman, died as a result of injuries sustained in the collision.
"The driver, a woman in her sixties, did not sustain life threatening injuries. There were no passengers on the bus when the collision occurred."
Police are urging witness to either incident to get in touch.
Two people have died in separate accidents involving buses in the Tayside area.