More than 30 sightings of Morag date back to 1887 and at least 16 involve multiple witnesses.
In 1948 "a peculiar serpent-like creature about 20ft long" was reported by nine people in a boat, in the same place as the original 1887 sighting.
The best known encounter, in 1969, involved Duncan McDonnel and William Simpson, and their speedboat, with which they claimed to have accidentally struck the creature, prompting it to hit back. Mr McDonnel retaliated with an oar, and Mr Simpson opened fire with his rifle, whereupon it sank slowly out of sight.
They described it as being brown, 25 to 30 feet long, and with rough skin. It had three humps rising 18 inches above the loch's surface, and a head a foot wide, held 18 inches out of the water.
The Loch Ness Investigation Bureau expanded its search to include Loch Morar in February 1970.
Several expeditions with the aim to prove or find the monster have been made, but no evidence for an unknown, large creature has been found.
Now a Canadian film crew are to investigate Morag for a series called Boogeymen.
They plan to film over three days at the end of next month and have appealed for eyewitnesses who say they have seen the monster - as well as those who doubt it has ever existed.
"For the show, I am looking for all good eyewitnesses, storytellers, believers and sceptics, scientists and historians who could tell us something about this story," said researcher Elizabeth Grenier for production company CMJ Productions II Inc.
"Boogeymen is an hour-long travel series that ventures to small, picturesque towns that have embraced something unusual and fascinating as their main attraction - a local monster!"