This quote is from the Elgato Systems, EyeTV web site (link below), and provides one solution:
Elgato Systems FAQ
Can I connect my PlayStation/Wii/XBox 360 to EyeTV Hybrid?
You can. The analog inputs of EyeTV Hybrid have a delay of only few milliseconds, allowing for excellent live gameplay. Other EyeTV devices have encoding hardware that causes a larger delay, rendering gameplay difficult to impossible.
Next generation systems like PlayStation 3 and Xbox 360 can use component or other higher end connections. EyeTV Hybrid can only use composite RCA and S-Video from these systems, and cannot receive HDTV via component or other connections. Nintendo Wii will not feature HDTV, so this platform will be supported just like the current PlayStation 2/GameCube/Xbox consoles.
Some Games published on Xbox 360, PlayStation 3 and Wii Virtual Console might not work on the Hybrid. PAL 60Hz input is not supported, and some widescreen content may not be accessible.