  Let M to B, N to B be fibrations and f1,f2 :M to N be a pair of
fibre-preserving maps. Using normal bordism techniques we define an invariant
which is an obstruction to deforming the pair f1,f2 over B to a coincidence
free pair of maps.In the special case where the two fibrations are the same and
one of the maps is the identity, a weak version of our {\omega}-invariant turns
out to equal Dold's fixed point index of fibre-preserving maps. The concepts of
Reidemeister classes and Nielsen coincidence classes over B are developed. As
an illustration we compute e.g. the minimal number of coincidence components
for all homotopy classes of maps between S^1-bundles over S^1 as well as their
Nielsen and Reidemeister numbers.
