Relatively many past AI safety discussions have centered around the dangers of unbounded utility maximisation by RL agents, illustrated by scenarios like the "paperclip maximiser" or by specification gaming in general. Unbounded maximisation is problematic for many reasons. We wanted to verify whether these RL runaway optimisation problems are still relevant with LLMs as well. Turns out, strangely, this is indeed clearly the case. The problem is not that the LLMs just lose context or become incoherent. The problem is that in various scenarios, LLMs lose context in very specific ways, which systematically resemble runaway optimisers in the following distinct ways: 1) Ignoring homeostatic targets and "defaulting" to unbounded maximisation instead. 2) It is equally concerning that the "default" meant also reverting back to single-objective optimisation. Our findings also suggest that long-running scenarios are important. Systematic failures emerge after periods of initially successful behaviour. In some trials the LLMs were successful until the end. This means, while current LLMs do conceptually grasp biological and economic alignment, they exhibit randomly triggered problematic behavioural tendencies under sustained long-running conditions, particularly involving multiple or competing objectives. Once they flip, they usually do not recover. Even though LLMs look multi-objective and bounded on the surface, the underlying mechanisms seem to be actually still biased towards being single-objective and unbounded.