1. A method executed on a server of a host securities broker from stored, computer-executable instructions for automatically trading a security in a sequence of transactions at a securities exchange, comprising the steps of: receiving a customer order over the Internet at the host securities broker to trade a security, the customer order comprising a first condition that specifies when to execute a first order for trading the security, and a second condition that specifies when to execute a second order for trading the security after the first condition has been satisfied; tracking at the host securities broker a current market price of the security: determining at the host securities broker whether the first condition has been satisfied; transmitting from the host securities broker the first order for execution at the securities exchange when the current market price satisfies the first condition; receiving at the host securities broker a confirmation of the execution of the first order; determining at the host securities broker whether the second condition has been satisfied; and transmitting from the host securities broker the second order for execution at the securities exchange when the current market price satisfies the second condition.