We review recent data on senescence and immortalization of human B-lymphoblastoid cell lines (LCLs) transformed by the Epstein-Barr virus (EBV). Although EBV-transformed LCLs are generally believed to be immortalized, a series of recent studies, including ours, provided strong evidence that they are mostly mortal and have non-malignant properties, except for a small proportion of LCLs that are immortalized by developing a strong telomerase activity. A large proportion of mortal LCLs have exceptionally long lifespans. Some of them have a lifespan over 150 population-doubling levels, keeping a relatively constant telomere length in spite of the absence of a detectable telomerase activity, suggesting that they maintain telomeres by a pathway other than that using telomerase. Here we propose a model of an alternative pathway to maintain telomeres of such long-lived mortal LCLs by exploiting extra-chromosomal telomere repeat DNA, which was recently found by us.