This proposal seeks support for continuation of Brookhaven National Laboratory experiment 791, a search for very rare decays of the neutral K meson. This experiment has had an engineering run and one physics run. Another physics run is anticipated this winter. Wojcicki was the spokesman for two years and remains in a leadership role. The experiment searches for K zero-long decaying into muon and electron (forbidden by lepton number conservation) and into muon and muon (suppressed by the standard model). The latter mode will be studied with good statistics; the former is a probe to mass scales much higher than can be achieved in direct reactions with current accelerators. An additional mode to be studied is into neutral pion, electron and positron. This is a CP violating decay; it is possible that direct CP violation may dominate in this decay.