Normal human somatic cells have a limited division potential when they grow in vitro. It is believed that shortening of telomeres, specialized structures at the ends of chromosomes, controls cell growth. When one telomere achieves a critical minimal length, the cell cycle control mechanism recognizes it as DNA damage and causes the cell's exit from the cycle in G1-phase. Because it is not possible to extend telomeres in normal cells, this non-dividing state is prolonged indefinitely, and is known as cellular senescence. The immortal cell line MDA-MB-231 has active telomerase, which prevents telomere shortening and allows cells' permanent divisions. However, there is a fraction of cells that do not divide over several days in culture as documented for some other tumour cell lines. Combination of methods has made it possible to isolate these non-growing cells and compare them with the fraction of fast-growing cells from the same culture. Although the non-growing fraction contains a significant percentage of typical senescent cells, both fractions have equal telomerase activity and telomere length. In this paper we discuss possible mechanisms that cause the appearance of this non-growing fraction of cells in cultures of MDA-MB-231, which indicate stress and genome instability rather than variation in telomerase activity or telomere shortening to affect individual cells.