  The purpose of this paper is to give some solutions for the classification
problem in fibration theory by using the homotopy sequences of fibrations
(sequences of $n$-th homotopy groups $ \pi_{n}(S,s_{o}) $ of total spaces of
fibrations). In particular, to show the role of homotopy sequence of $n$-th
homotopy to get the required fiber map in Fadell-Dold theorem such that the
restriction of this fiber map on some fiber spaces is a homotopy equivalence.
