We develop a formalism to study the influence of the breakup process o
f a weakly bound projectile on the complete fusion cross section. We s
how that the complete fusion and the resulting incomplete fusion cross
sections can be expressed in terms of breakup and survival probabilit
ies, which are evaluated with the help of appropriate polarization pot
entials. The effects of the finite size of the projectile and of Fermi
motion are estimated. As examples, we consider light-heavy-ion collis
ions where threshold effects play an interesting role.