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In PET imaging, listmode is an alternative for projections to store the acquisition data with more accuracy. The reconstruction starting from the listmode format requires different approaches from projection based algorithms. The ML-EM algorithm was modified to start from the listmode format. For listmode data image degrading effects can be classified into two groups. Internal LOR effects (like attenuation, detection efficiency) do not lead to another LOR than the correct one, but only lead to a lower detection efficiency along the correct LOR. The correction for these effects can be done by using a sensitivity factor in the iterative algorithm. On the other hand there are also external LOR effects (scatter, randoms, resolution) which do lead to detection of wrong LORs. The correction for these effects can in principle be done by modifying the system matrix used in iterative reconstruction. For listmode reconstruction this system matrix can not be precalculated because of the very high number of possible LORs. Therefore we combined a simple model (Siddon) for the forward and backprojection with a depth dependent blurring function for the close range external LOR effects. It is shown how the resolution varies with the distance from the detector and how this effect can be modelled efficiently in combination with the Siddon algorithm. Effects like scatter and randoms are corrected by using an additive term for the forward projection. We show how the number of randoms along a LOR is estimated from the singles distribution and how this effect is corrected by the additive term in the listmode reconstruction.