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Thanks for asking.
In general, Remote Buddy gives you full flexibility in how to use 
supported remotes. Sure enough, you can use Remote Buddy with a 
supported remote control to control EyeTV and also access and control 
EyeTV's built-in menu, if you so wish. For a list of supported 
remotes, please check the Remote Buddy website.
If you want to use an EyeTV Remote, however, it really depends on what 
exact hardware models you are using / want to use respectively. The 
easiest way to find out there is to simply start up EyeTV, start up 
Remote Buddy and press a button. If your EyeTV remote now shows up in 
Remote Buddy Prefs > Hardware, it is supported. If your EyeTV Remote 
does not show up in Remote Buddy's prefs > Hardware, it is not 
supported.
Since you don't provide details on any of the hardware, however, I 
can't give you any definitve answer. If you already have all 
components in place, the easiest way for you to find out whether you 
can do all the things you want to do is to make use of the free, 
feature-unlimited 30 day trial time of Remote Buddy prior to making a 
purchase.
Best regards, 
Felix Schwarz