Mehdi studied (ω+k)-projective QTAG-modules with the help of their submodules contained in Hk(M) (the submodule generated by the elements of exponents at most k). These modules contain nice submodules N contained in Hk(M) such that M/N is a direct sum of uniserial modules. Here, we investigate the class of QTAG-modules, containing nice submodules N⊆Hk(M) such that M/N is totally projective. We also study strong ω-elongation of totally projective QTAG-modules by (ω+k)-projective QTAG-modules. ; Mathematics subject classification (2000) : 16 K 20