Non-Space was a void of infinite nothingness, where time does not exist. Under normal circumstances, spaceships were not able to enter non-space, although some GELF species had somehow found a way to do this.
As the Dwarfers walked down the linkway, Kryten said that the linkway was as stable as an Italian taxi driver who had got stuck behind two old priests in a Skoda. This was demonstrated when part of the linkway gave way beneath the Cat's feet, although Dave Lister and Kryten were able to catch him before he fell into the non-space outside the linkway. The non-space appeared as an inky blackness filled with fast-slowing ribbons of white mist.
After meeting their alternate counterparts from the other dimension, including a version of Kristine Kochanski who had survived the radiation leak aboard Red Dwarf, a Kinitawowi battle cruiser somehow infiltrated non-space and began to shoot energy blasts at the linkway. The linkway was severed and Kochanski fell into non-space, although she was saved by grabbing onto some dental floss which Lister had been unable to remove from his teeth earlier in the day.
Starbug then fled the area of space with the dimensional tear, and the GELF battle cruiser left non-space and gave chase down to the surface of an ice moon. With the help of expert navigation officer Kochanski, they were able to goad the cruiser into crashing on the surface. Kochanski then endeavored to restore the linkway using electromagnetic phasing frequencies so that she could rejoin her own crew.
As Kochanski was reunited with her own crew, a second GELF battle cruiser appeared in non-space and broke the linkway again, separating Kochanski back with the Dwarfers. She attempted to jump back to her own crew, but missed the other part of the broken linkway by mere centimeters, and she fell into non-space once again. Kochanski's crew had to restrain the hologram Lister from jumping in after her.
The Dwarfers ran back to Starbug to look for anything which may help retrieve Kochanski, and found some mountaineering equipment and rope they had swapped with Kochanski's crew - including a crossbow. Lister ran back into the broken linkway and fired a bolt which pierced Kochanski's leg just before she went completely out of range. As they hoisted her back up to safety, she called Lister on his communicator with an obscene phone call. ("Ouroboros", Series VII)