  We report a microscopic model wherein the unconventional superconductivity
emerges from an incoherent `Cooper-pair glass' state. Driven by the pair-pair
interaction, a new type of quasi-Bose phase transition is at work. The
interaction leads to the unconventional coupling of the quasiparticles to
excited pair states, or `super-quasiparticles', with a non-retarded
energy-dependent gap. The model describes quantitatively the quasiparticle
excitation spectra of both cuprates and pnictides, including the universal
`peak-dip-hump' signatures, and for the pseudogap phase above $T_c$. The
results show that instantaneous pair-pair interactions account for the SC
condensation without a collective mode.
