I set up a noninverting amplfier with ±15V supplies and symmetrical (±V) square wave inputs of various amplitudes. Depending on amplitude and gain, the output would sometimes "blow up" and soar exponentially to megavolts. Sometimes the output would set at ≈-19V, with tiny impulses on the output when the input transitioned.
I played with it some more just now. It works or blows up depending on input levels and. closed loop gain. In one case, it worked with ±200mV square wave in and Rf=500k, Rs=10k, but not with Rf=50k, Rs=1k.
Attached is a zip file that should allow you to see for yourself what I see. If you run it and get good results, or find out what I am doing wrong, or find a spice tweak that fixes it, let us know.