Given a flbre homotopy
equivalence ϕ over B of flbre spaces E and F which have the Weak Covering
Homotopy Propeny (WCHP), it is shown that ϕ has a generalized mapping
cylinder which also possesses the WCHR The ordinary topological mapping
cylinder M(ϕ) as a space over [0,1] × B does not necessarily possess the
WCHP.