In this paper, we investigate the limit points set of surjective and approximate point spectra of upper triangular operator matrices . We prove that σ*(MC) ∪ W=σ*(A)∪ σ*(B) where W is the union of certain holes in σ*(MC), which happen to be subsets of σ lgD(B) ∩ σrgD(A), σ* ∈ {σlgD, σrgD}  are the limit points set of surjective and approximate point spectra. Furthermore, several sufficient conditions for σ* (MC) = σ* (A)∪σ* (B) holds for every C ∈ ℬ(Y,X) are given.