  The theory for condensation of higher fermionic clusters is developed. Fully
selfconsistent nonlinear equations for the quartet order parameter in strongly
coupled fermionic systems are established and solved. The breakdown of the
quasiparticle picture is pointed out. Derivation of numerically tractable
approximation is described. The momentum projected factorisation ansatz of Ref.
\cite{slr09} for the order parameter is employed again. As a definite example
the condensation of $\alpha$ particles in nuclear matter is worked out.
