  In this paper we investigate various properties of generalised pairs in
families, especially boundedness of several kinds. We show that many statements
for usual pairs do not hold for generalised pairs. In particular, we construct
an unexpected counter-example to boundedness of generalised lc models with
fixed appropriate invariants. We also show that the DCC of Iitaka volumes and
existence of nef reduction maps fail in families of generalised pairs. In a
positive direction we show boundedness of bases of log Calabi-Yau fibrations
with their induced generalised pair structure under natural assumptions.
Roughly speaking we prove this boundedness for fibrations whose general fibres
belong to a bounded family and whose Iitaka volume is fixed.
