UweBonnes,
With really high speed op amps, a large feedback resistor with the op amp input capacitance will give you a pole. Change the 1k/10k resistors to 220/2.2k and see if the frequency of oscillation changes.
Where does "SO" go? It's hard to read your schematic; is the resistor from "SO" to ground not populated?
The 470 might be too low for the AD8065 to drive depending on where it goes.
Harry