  We show that in a fibration the coformality of the base space implies the
coformality of the total space under reasonable conditions, and these
conditions can not be weakened. The result is partially dual to the classical
work of Lupton \cite{Lup} on the formality within a fibration. Our result has
two applications. First, we show that for certain cofibrations, the coformality
of the cofiber implies the coformality of the base. Secondly, we show that the
total spaces of certain spherical fibrations are Koszul in the sense of
Berglund \cite{Ber}.
