I watched Lifeforce (1985) the other day. It's about a crew of astronauts that discovered an alien ship hidden within the tail of Halley's Comet. Littered all over the ship, there were countless corpses of creatures resembling giant bats as well as three humanoid beings inside crystal coffins. The crew decided to retrieved the bodies and bring them back to Earth, unbeknown to the world ending horror they were about to unleash.
The last act of the movie features a full blown zombie apocalypse in the burning ruins of London. The surprising thing was that the incredibly fast and violent zombies had more in common with the infected from 28 Days Later (2002) than with their contemporary brethren.
Keep in mind that Lifeforce predates Return of the Living Dead (1985), the movie often cited as the first one to introduced this kind of zombie, for a couple of months.
Is Lifeforce the first movie to feature the running dead or is this concept even older?