If you have an oscillation in a circuit, it is no longer linear!
Sounds like a typical AD797 oscillation. GBWs of OP27 and AD797 are 8MHz and 110MHz, respectively. OP27 can't make such high freq oscillation.
I didn't check the circuit diagram. Usually AD797 has ~5pF feedback capacitance to increase the stability. You may be able to stop the oscillation by adding/replacing a mica capacitor from 10~470pF. But 50% of the time the oscillation is not fixed with this kind of modification. You need a cut-and-try.