  This work treats on the question whether a given map f: M -> B of smooth
closed manifolds is homotopic to a smooth fiber bundle. We define a first
obstruction in H^1(B;Wh(\pi_1(E))) and, provided that this obstruction vanishes
and one additional condition is verified, a second obstruction in Wh(\pi_1(E))
>. Both elements vanish if the answer to the above question is positive. In the
case where B is the 1-sphere and the dimension of M exceeds five, we show that
the converse is also true, using a relationship with two obstructions defined
by Farrell in this particular situation.
