  We present a polynomial-time algorithm minimising the number of states of
history-deterministic generalised coB\"uchi automata, building on the work of
Abu Radi and Kupferman on coB\"uchi automata. On the other hand, we establish
that the minimisation problem for both deterministic and history-deterministic
generalised B\"uchi automata is NP-complete, as well as the problem of
minimising at the same time the number of states and colours of
history-deterministic generalised coB\"uchi automata.
