The twin blazes, both believed to have been caused by mechanical problems, brought the number of Rome buses destroyed by fire so far this year to 10.
Some 20 buses operated by local transport company Atac were burnt out in 2017.
The drivers of both buses in yesterday’s incidents managed to escape with their passengers unscathed, although a woman who worked in a nearby shop suffered minor burns when one of the two vehicles exploded in central Rome.
The number 63 bus came to a halt near the Trevi Fountain, a popular tourist attraction, before the fire took hold.
Video showed flames shooting into the sky and the facades of the two nearest buildings were left smeared with black soot.
Hours later a bus full of students caught fire near a school in the southwestern suburb of Castel Porziano, the Il Messaggero newspaper reported, publishing a video clip of the incident.
“It’s not ISIS [Islamic State], it’s ATAC. Which is worse,” one Twitter user wrote, one of many who mockingly compared the extremist group to Rome’s beleaguered public transport company.
“ISIS ANNOUNCES A CHANGE OF NAME TO ATAC: ‘IT IS MUCH MORE TERRIFYING’,” Luca Bottura, a satirist who writes for La Repubblica daily, wrote on Twitter.
It is not the first time that Romans have used this kind of black humour: A joke has long been doing the rounds about the city being impenetrable to Islamic State because of its infamous potholes and gridlocked traffic.
Atac said that the first bus that caught fire was 15 years old and was “completely destroyed”.
An internal enquiry will investigate the causes of the accident, it added.
Politicians were quick to blame Mayor Virginia Raggi and her party, the anti-establishment 5-Star Movement (M5S), for the series of fires, saying that it showed they were incapable of governing Rome.
“Romans risk getting hurt every day with this 5-Star administration,” said Barbara Saltamartini, a member of the far-right League party. “These images are being seen around the world and they are the latest images of Raggi’s failure.”
M5S says it inherited a transport system that was mired in debt and dragged down by poor management and that it is working hard to overcome numerous long-standing problems.
A former head of Atac said last year that the company was suffocating under some €1.3bn ($1.54bn) of debts and should declare bankruptcy.
According to an internal Atac report, 36% of all the company’s buses are in garages because they have broken down or are undergoing maintenance, with the figure rising to 50% for the city’s creaking fleet of trams.