The infinite zero structure of linear multivariable systems is investigated via the geometric approach. The basic tools used are the new concepts of almost (A, B)-invariant and almost controllability subspaces. These concepts permit advantageous geometric interpretation of infinite zeros. This interpretation is a natural generalization of the finite case. Connection is made with the Smith McMillan structure at infinity of the transfer matrix. Structural properties of irreducible systems are investigated leading to a generalization of Morse theorem on prime systems.