Context : The pulsation periods of long period variables ( LPVs ) depend on their mass and helium abundance as well as on their luminosity and metal abundance .
Comparison of the observed periods of LPVs in globular clusters with models is capable of revealing the amount of mass lost on the giant branch and the helium abundance .

Aims : We aim to determine the amount of mass loss that has occurred on the giant branches of the low metallicity globular clusters NGC 362 and NGC 2808 .
We also aim to see if the LPVs in NGC 2808 can tell us about helium abundance variations in this cluster .

Methods : We have used optical monitoring of NGC 362 and NGC 2808 to determine periods for the LPVs in these clusters .
We have made linear pulsation models for the pulsating stars in these clusters taking into account variations in mass and helium abundance .

Results : Reliable periods have been determined for 11 LPVs in NGC 362 and 15 LPVs in NGC 2808 .
Comparison of the observed variables with models in the \log P – K diagram shows that mass loss of \sim 0.15–0.2 M _ { \odot } is required on the first giant branch in these clusters , in agreement with estimates from other methods .
In NGC 2808 , there is evidence that a high helium abundance of Y \sim 0.4 is required to explain the periods of several of the LPVs .

Conclusions : It would be interesting to determine periods for LPVs in other Galactic globular clusters where a helium abundance variation is suspected to see if the completely independent test for a high helium abundance provided by the LPVs can confirm the high helium abundance estimates .