  Ivanov and Tuzhilin started an investigation of a particular case of Gromov
Minimal Fillings problem (generalized to the case of stratified manifolds).
Weighted graphs with non-negative weight function were used as minimal fillings
of finite metric spaces. In the present paper we introduce generalized minimal
fillings, i.e. minimal fillings where the weight function is not necessarily
non-negative. We prove that for any finite metric space its minimal filling has
the minimum weight in the class of all generalized fillings of the space.
