As a generalization of the concept of pseudo-biorthogonal bases (PBOB), we already presented in Ref. [3] the theory of the so-called extended pseudo-biorthogonal bases (EPBOB). We introduce in this paper two special types of EPBOB called EPBOB's of type O and of type L. This paper discusses characterizations, construction methods, inherent properties, and mutual relations of these types of EPBOB.