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I agree with KlausST. I don't think it is stable. At high frequencies, first opamp sees a local positive feed back making it unstable. However, simulating it would be a good test to arrive at any conclusion.
I visualize the given opamp configuration as "Two stage Opamp design with Miller Cap compensation".
I have attached the reference image.
Since the added Cc introduces a "Right hand side zero" the phase margin can be less than required.
So, it has a higher possibility to oscillate.
To make it stable try to place a "Resistor"in series with Cc. The value of resistor can be greater than the inverse of the input trans-conductance of second opamp. Getting this info may not be possible, so try to fix it through simulation.
With or without the capacitor - the circuit is not stable.
For dc you have negative feedback - hence the whole system will find a stable quiescent operational point.
However, two opamps in a closed loop result in a loop gain magnitude function with a slope of at least -40dB/dec at the cross-over frequency (0 db gain).
This violates the stability criterion.
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