Abstract. I introduce and study new derivative securities which I call game options (or Israeli options to put them in line with American, European, Asian, Russian etc. ones). These are contracts which enable both their buyer and seller to stop them at any time and then the buyer can exercise the right to buy (call option) or to sell (put option) a specified security for certain agreed price. If the contract is terminated by the seller he must pay certain penalty to the buyer. A more general case of game contingent claims is considered. The analysis is based on the theory of optimal stopping games (Dynkin's games). Game options can be sold cheaper than usual American options and their introduction could diversify financial markets.