  We study relative log canonical pairs with relatively trivial log canonical
divisors. We fix such a pair $(X,\Delta)/Z$ and establish the minimal model
theory for the pair $(X,\Delta)$ assuming the minimal model theory for all
Kawamata log terminal pairs whose dimension is not greater than ${\rm dim}\,Z$.
We also show the finite generation of log canonical rings for log canonical
pairs of dimension five which are not of log general type.
