Abstract: The present paper presents the definition of the stopping for two-parameter strong martingale and deals with the stopping properties for two-parameter strong martingale. It has been proved that the stopping for strong martingale is still strong martingale, the stopping for square integrable strong martingale is still square integrable strong martingale, the stopping for uniform integrable martingale is still uniform integrable strong martingale.

Key words: strong martingale, stopping, property