Given CW-complexes X, \(Y_ 1,\dots,Y_ n\). The problem is to classify, up to homotopy, the towers \[ f: X_ n \overset{f_ n}\longrightarrow X_{n-1} \longrightarrow \cdots \longrightarrow X_ 1 \overset{f_1}\longrightarrow X \] of (Serre) fibrations of CW-complexes such that for all \(i=1,\dots,n\) the fibre of \(f_ i\) has the weak homotopy type of \(Y_ i\). A map \(f\to f'\) of two towers is a commutative diagram \[ \begin{matrix} X_ n & \overset{f_n}\longrightarrow & X_{n-1} & \longrightarrow & \cdots & \longrightarrow & X_1 & \overset{f_1}\longrightarrow & X \\ \\ \downarrow && \downarrow &&&& \downarrow && \downarrow_{\text{id}} \\ \\ X'_ n & \overset{f'_ n}\longrightarrow & X'_{n-1} & \longrightarrow & \cdots & \longrightarrow & X_1' & \overset{f'_1}\longrightarrow & X. \\ \end{matrix} \] If all vertical maps are homotopy equivalences then the map \(f\to f'\) is called a homotopy equivalence of towers. \(BEY_ i\) (resp. BEf) denotes the classifying space of the monoid \(EY_ i\) (resp. Ef) of homotopy self equivalences of the space \(Y_ i\) (resp. of the tower f). The authors construct inductively a homotopical wreath product \(B(EY_ 1,\dots,EY_ n)\) which classifies the towers as above up to homotopy, where the path component of \(B(EY_ 1,\dots,EY_ n)^ X\) determined by f has the homotopy type of BEf. The infinite wreath product \(B(EY_ 1,\dots,EY_ n,\dots)\) is defined by passing to the inverse limit. In the special case of Eilenberg-MacLane spaces \(Y_ i=K(G_ i,i)\), \(i=1,2,\dots\), this limit space classifies up to homotopy the connected CW-complexes Y such that \(\pi_ iY\cong G_ i\), where the component of \(B(EY_ 1,\dots,EY_ n,\dots)^ X\) corresponding to Y has the homotopy type of BEY. Of course the authors actually prove equivalent simplicial results.