One of the fundamental ideas investigated in A. Ammar, A. Jeribi and K. Mahfoudhi in \cite{kam} is that of providing conditions under which the essential approximate pseudospectrum of closed, densely defined linear operators have a relationship with Fredholm theory and perturbation theory. In this paper the approximate pseudospectrum and the essential approximate pseudospectrum of closed, densely defined multivalued linear relations are introduced and studied, and work done in the aforementioned papers are extended to general multivalued linear relations