The future neutrino telescope KM3NeT, to be built in the Mediterranean Sea, will be the largest of its kind. It will include nearly two hundred thousand photomultiplier tubes (PMT) mounted in multi-PMT digital optical modules (DOM). The dominant source of the PMT signals is decays of 40K and marine fauna bioluminescence. Selection of neutrino and muon events from this continuous optical background signals requires the implementation of fast and efficient triggers. Various schemes for the filtering of background data and the selection of neutrino and muon events were evaluated for the KM3NeT telescope using Monte Carlo simulations.