It is argued that the response function of a liquid of interacting particles containing a condensate fraction has a nonvanishing width at the quasielastic peak, unlike the otherwise expected \ensuremath{\delta}-function peak for a noninteracting system. The mechanism involved is the scattering of the particles in the system, implying the effect is a many-body one. For systems with regular interactions between the particles, the width vanishes in the asymptotic limit of momentum transfer q\ensuremath{\rightarrow}\ensuremath{\infty}, leading to a \ensuremath{\delta}-function peak in the response, while for singular interactions such as a hard core, a nonzero width remains. The methods used in the argument can be applied to derive a general class of theories describing final-state interactions. The Gersch-Rodriguez broadening formula is derived using these methods.