When telomeres are rendered dysfunctional through replicative attrition of the telomeric DNA or by inhibition of shelterin, cells show the hallmarks of ataxia telangiectasia mutated (ATM) kinase signalling. In addition, dysfunctional telomeres might induce an ATM-independent pathway, such as ataxia telangiectasia and Rad3-related (ATR) kinase signalling, as indicated by the phosphorylation of the ATR target CHK1 in senescent cells and the response of ATM-deficient cells to telomere dysfunction. However, because telomere attrition is accompanied by secondary DNA damage, it has remained unclear whether there is an ATM-independent pathway for the detection of damaged telomeres. Here we show that damaged mammalian telomeres can activate both ATM and ATR and address the mechanism by which the shelterin complex represses these two important DNA damage signalling pathways. We analysed the telomere damage response on depletion of either or both of the shelterin proteins telomeric repeat binding factor 2 (TRF2) and protection of telomeres 1 (POT1) from cells lacking ATM and/or ATR kinase signalling. The data indicate that TRF2 and POT1 act independently to repress these two DNA damage response pathways. TRF2 represses ATM, whereas POT1 prevents activation of ATR. Unexpectedly, we found that either ATM or ATR signalling is required for efficient non-homologous end-joining of dysfunctional telomeres. The results reveal how mammalian telomeres use multiple mechanisms to avoid DNA damage surveillance and provide an explanation for the induction of replicative senescence and genome instability by shortened telomeres.