Preservation of homotopical structures by localization functors is a classical question in homotopy theory. In this paper the authors obtain necessary and sufficient conditions for a fibration sequence to be preserved by a nullification functor. Also, nullification functors \(L=P_W\) are characterized among localization functors \(L_f\) defined by formally inverting a map \(f\colon A\to B\) (see [\textit{A. K. Bousfield}, J. Am. Math. Soc. 7, No.~4, 831--873 (1994; Zbl 0839.55008)], [\textit{E. Dror Farjoun}, Cellular spaces, null spaces and homotopy localization. Lecture Notes in Mathematics. 1622. (Berlin: Springer-Verlag). (1995; Zbl 0842.55001)] for definitions, properties, and examples of such functors). Whether or not all localization functors are of the form \(L=L_f\) depends on the axioms of set theory under consideration [\textit{C. Casacuberta, D. Scevenels} and \textit{J. H. Smith}, Implications of large-cardinal principles in homotopical localization. Adv. Math. (in Press, available online.)] Let \(L=P_W\) be a nullification functor. For a given space \(X\), \(A_LX\) stands for the homotopy fibre of the coaugmentation \(l_X\colon X\to LX\) and \(d_X\colon A_LX\to X\) for the induced map. If \[ F \;\mathop{\longrightarrow} \;E \;\mathop{\longrightarrow}^p \;B \tag{1} \] is a fibration sequence and \[ F \;\mathop{\longrightarrow} \;E_1 \;\mathop{\longrightarrow}^q \;A_LB \tag{2} \] the pullback fibration along \(d_X\), the main theorem states that (1) is preserved by \(L\) if and only if (2) is preserved by \(L\) if and only if (2) is fibre homotopically trivial. A cohomological criterion is obtained as a corollary for \(F\), \(E\), and \(B\) connected in (1); namely, if \(LF\) is nilpotent, \(\pi_1(A_LB)\) acts nilpotently on the integral homology groups of \(F\), and \(A_LB\) is acyclic, then, (1) is preserved by \(L\). Similar results in different homology theories would be interesting.