Individuals who claim links to a world-wide network of fringe-belief supporters and conspiracy theorists are thought to be behind the daubing of messages on signs along the length of the A9.
The slogans “Flat Earth” and “The Earth is flat” have sprung up on the rear of numerous road signs throughout Highland Perthshire.
A large and rusty advertising hoarding has also been erected by the side of the road near Dowally in Highland Perthshire.
It urges passing motorists to “Research Flat Earth”, replacing an earlier message that also asked people to adopt the unusual view of the world.
Flat earth societies are nothing new having been around for hundreds of years but in recent months they have experienced something of an online resurgence.
In their contentious view of the universe, the notion of a globe-shaped world orbiting the sun is nothing but a myth.
A variety of competing groups and individuals exist, many deadly serious and others apparently just in the argument for fun.
Some more hard-core flat-earthers have been linked to a number of other fringe views and some more unpalatable viewpoints, including Antisemitism.
A number of the larger groups have been vying to be the “official” body representing the beliefs – leading to significant disagreement.
It is not known who is behind the Perthshire slogans and sign. Police Scotland said the messages had only just been brought to their attention.
A spokeswoman said: “Vandalism is unacceptable no matter what form it takes. It creates unnecessary expense for individuals and organisations.
“Where offences are reported to Tayside Division it will carry out appropriate enquiries and where offenders are identified they will be robustly dealt with.
“Police Scotland urges people not to tolerate vandalism or anti-social behaviour but to report them immediately.”
The flat earth messages are repeated on the rear of a number of road signs between Perth and Dalwhinnie.