  We prove the existence of a Quillen Flat Model Structure in the category of
unbounded complexes of h-unitary modules over a nonunital ring (or a
$k$-algebra, with $k$ a field). This model structure provides a natural
framework where a Morita-invariant homological algebra for these nonunital
rings can be developed. And it is compatible with the usual tensor product of
complexes. The Waldhausen category associated to its cofibrations allows to
develop a Morita invariant excisive higher $K$-theory for nonunital algebras.
