Before this Wireless N Adapter became available, you can only connect your Xbox 360 to a Wireless G Network using the older Wi-Fi adapter. You can also use the Ethernet port for a wire network if you do the cabling. But, purchasing a special Ethernet-to-Wireless N bridge can also help if …

Learn how to configure wireless settings on your Xbox 360 Note You can use an Xbox 360 Wireless Networking Adaptor with the Xbox 360 E console. If your wireless router is not near your console, you may get a better wireless signal by using a wireless networking adaptor. When you connect an Xbox 360 Wireless Networking Adaptor to an Xbox 360 E console, the console automatically uses the wireless adaptor instead of the built-in WiFi. Can you connect XBOX 360 to a wireless WiFi network Nov 26, 2012

The built-in wi-fi on XBOX360 models that have that feature does uses only the 2.4ghz spectrum. I have read reports that the black XBOX 360 N adaptor does support 5ghz but I find that quite dubious since mine clearly does not and I found no product literature that says otherwise when I searched.

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Xbox 360 fails to connect to network - here is the fix Sep 17, 2015