This paper provides examples which can not be approximate fibrations and shows that if $N^n$ is a closed aspherical manifold, $pi_1(N)$ is hyperhophian, normally cohophian, and $pi_1(N)$ has no nontrivial Abelian normal subgroup, then the product of $N^n$ and a sphre $S^m$ satisfies the property that all PL maps from an orientable manifold M to a polyhedron B for which each point preimage is homotopy equivalent to $N^n imes S^m$ necessarily are approximate fibrations.