This invention discloses a method for connecting a media stream, which includes: transmitting, by a media gateway in a private network, a connecting message to an external network device through a network address translation device; the connecting message is used for generating a new address mapping, which is used for a subsequent media stream to pass through the network address translation device, in the network address translation device when there is no address mapping available in the network address translation device; and the connecting message is used for keeping alive an address mapping when the address mapping is already available in the network address translation device. The invention further discloses a system for connecting a media stream, two methods for detecting connectivity, and a system for detecting connectivity.