No consensus exists so far on the definition of cellular senescence. The narrowest definition of senescence is irreversible growth arrest triggered by telomere shortening counting cell generations (definition 1). Other authors gave an enlarged functional definition encompassing any kind of irreversible arrest of proliferative cell types induced by damaging agents or cell cycle deregulations after overexpression of proto-oncogenes (definition 2). As stress increases, the proportion of cells in "stress-induced premature senescence-like phenotype" according to definition 1 or "stress-induced premature senescence," according to definition 2, should increase when a culture reaches growth arrest, and the proportion of cells that reached telomere-dependent replicative senescence due to the end-replication problem should decrease. Stress-induced premature senescence-like phenotype and telomere-dependent replicatively senescent cells share basic similarities such as irreversible growth arrest and resistance to apoptosis, which may appear through different pathways. Irreversible growth arrest after exposure to oxidative stress and generation of DNA damage could be as efficient in avoiding immortalisation as "telomere-dependent" replicative senescence. Probabilities are higher that the senescent cells (according to definition 2) appearing in vivo are in stress-induced premature senescence rather than in telomere-dependent replicative senescence. Examples are given suggesting these cells affect in vivo tissue (patho)physiology and aging.