  The 2-parameter Green functions occur as a crucial ingredient in the
character formula for Lusztig induction in finite reductive groups. Still, very
little is known about these functions, in particular in the case of groups
arsing from algebraic groups with disconnected centre. We collect some basic
properties and then apply these, together with some explicit computations, to
determine all 2-parameter Green functions for 8-dimensional spin groups in odd
characteristic, whose centre is disconnected of order~4.
