Coincidence points of fiber maps on Sn-bundles

In this note we study coincidence of pairs of fiber-preserving maps f,g:E1→E2 where E1,E2 are Sn-bundles over a space B. We will show that for each homotopy class [f] of fiber-preserving maps over B, there is only one homotopy class [g] such that the pair (f,g), where [g]=[τ○f] can be deformed to a coincidence free pair. Here τ:E2→E2 is a fiber-preserving map which is fixed point free. In the case where the base is S1 we classify the bundles, the homotopy classes of maps over S1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem.