I've put hysteresis in op-amp circuits with a diode that puts current through an additional feedback resistor.
Capacitors to delay response. This was an overload detector that shut off an RF amp if it failed to reach intended amplitude in circuit (e.g. due to mismatch.)
I also learned that there are "comparator" ICs which while similar to op-amp, behave a bit differently.
If an op-amp is allowed to rail its output, some latch up or take an indeterminate amount of time to recover. They also transfer power supply noise, even to other amps in the same package (PSRR is reduced).
Op-amps can have better input-offset stability.
Comparators can be faster recovering from railed condition (which is their normal use)
After learning this, I modified my circuit so op-amp was kept out of saturation rather than railing (only one polarity needed to be clean, because the other disabled operation.)